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Analysis und Systemtheorie


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Prof. Dr. Achim Ilchmann

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Mehrez, Mohamed W.; Worthmann, Karl; Mann, George K.I.; Gosine, Raymond G.; Pannek, Jürgen
Experimental speedup and stability validation for multi-step MPC. - In: IFAC-PapersOnLine. - Frankfurt : Elsevier, ISSN 24058963, Bd. 50 (2017), 1, S. 8698-8703
https://doi.org/10.1016/j.ifacol.2017.08.1551
Mehrez, Mohamed W.; Worthmann, Karl; Mann, George K.I.; Gosine, Raymond G.; Faulwasser, Timm
Predictive path following of mobile robots without terminal stabilizing constraints. - In: IFAC-PapersOnLine. - Frankfurt : Elsevier, ISSN 24058963, Bd. 50 (2017), 1, S. 9852-9857
https://doi.org/10.1016/j.ifacol.2017.08.907
Braun, Philipp; Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.; Worthmann, Karl
Towards price-based predictive control of a small-scale electricity network. - In: International journal of control. - London : Taylor & Francis, ISSN 13665820, (2017), published online (28. Jun.), insges. 22 S.
https://doi.org/10.1080/00207179.2017.1339329
Ioan, Daniel-Mihail; Stoican, Florin; Worthmann, Karl
Active fault detection and isolation in a zonotopic framework. - In: IEEE Xplore digital library. - New York, NY : IEEE, (2017), S. 595-600
https://doi.org/10.1109/ICSTCC.2017.8107100
Hasse, Seppo; Sandovici, Adrian; Snoo, Henk S. V.; Winkler, Henrik
Extremal maximal sectorial extensions of sectorial relations. - In: Indagationes mathematicae. - Amsterdam : Elsevier, Bd. 28 (2017), 5, S. 1019-1055
https://doi.org/10.1016/j.indag.2017.07.003
Behrndt, Jussii; Schmitz, Philipp; Trunk, Carsten
Spectral bounds for singular indefinite Sturm-Liouville operators with L1-potentials. - Ilmenau : Technische Universität, Institut für Mathematik. - 1 Online-Ressource (7 Seiten). - (Preprint. - M17,12)
Im Titel ist "1" hochgestellt

The spectrum of the singular indefinite Sturm-Liouville operator A=sgn(.) (-d^2/dx^2)+q with a real potential q in L^1(R)$ covers the whole real line and, in addition, non-real eigenvalues may appear if the potential q assumes negative values. A quantitative analysis of the non-real eigenvalues is a challenging problem, and so far only partial results in this direction were obtained. In this paper the bound l lambda | <= |q|_{L^1}^2 on the absolute values of the non-real eigenvalues lambda of A is obtained. Furthermore, separate bounds on the imaginary parts and absolute values of these eigenvalues are proved in terms of the L^1-norm of q and its negative part q_-.


http://nbn-resolving.de/urn:nbn:de:gbv:ilm1-2017200509
Behrndt, Jussii; Gsell, Bernhard; Schmitz, Philipp; Trunk, Carsten
An estimate on the non-real spectrum of a singular indefinite Sturm-Liouville operator. - Ilmenau : Technische Universität, Institut für Mathematik. - 1 Online-Ressource (5 Seiten). - (Preprint. - M17,10)

It will be shown with the help of the Birman-Schwinger principle that the non-real spectrum of the singular indefinite Sturm-Liouville operator $\operatorname{sgn}(\cdot)(-\mathrm d^2/\mathrm d x^2 +q)$ with a real potential $q\in L^1\cap L^2$ is contained in a circle around the origin with radius $\|q\|_{L^1}^2$.


https://www.db-thueringen.de/receive/dbt_mods_00032787
Berger, Thomas; Gernandt, Hannes; Trunk, Carsten; Wojtylak, Micha&lstrok;
New lower bound for the distance to singularity of regular matrix pencils. - Ilmenau : Technische Universität, Institut für Mathematik. - 1 Online-Ressource (5 Seiten). - (Preprint. - M17,10)

For regular matrix pencils $\Ac(s)=sE-A$ the distance to the nearest singular pencil in the Frobenius norm of the coefficients is called the distance to singularity. We derive a new lower bound for this distance by using the spectral theory of tridiagonal Toeplitz matrices.


https://www.db-thueringen.de/receive/dbt_mods_00032786
Bergmann, Jean Pierre; Bielenin, Martin; Herzog, Roland A.; Hildebrand, Jörg; Riedel, Ilka; Schricker, Klaus; Trunk, Carsten; Worthmann, Karl
Prevention of solidification cracking during pulsed laser beam welding. - Ilmenau : Technische Universität, Institut für Mathematik. - 1 Online-Ressource (7 Seiten). - (Preprint. - M17,05)

We present a mathematical model to describe laser beam welding based on the heat equation. Since the material coeff cients depend on the temperature, this leads to a quasi-linear parabolic partial differential equation. It is our goal to prevent solidif cation cracking. We address this problem by means of optimal control. It is the intensity prof le of the laser beam which acts as the control function. The main challenge is the formulation of a suitable objective function. In particular, high velocities of the solidif cation interface need to be properly penalized in order to deal with and avoid cracking phenomena.


https://www.db-thueringen.de/receive/dbt_mods_00032771
Gernandt, Hannes; Krauße, Dominik; Sommer, Ralf; Trunk, Carsten
A new method for network redesign via rank one updates. - Ilmenau : Technische Universität, Institut für Mathematik. - 1 Online-Ressource (5 Seiten). - (Preprint. - M17,05)

We present a method to place the eigenvalues of an electrical network towards a prescribed set of complex numbers by inserting an additional capacitance into the network. We use recent results on rank one perturbations of regular matrix pencils and provide an upper bound on the approximation error of the eigenvalues in the chordal distance.


https://www.db-thueringen.de/receive/dbt_mods_00032770
Worthmann, Karl; Mehrez, Mohamed W.; Mann, George K. I.; Gosine, Raymond G.; Pannek, Jürgen
Interaction of open and closed loop control in MPC. - In: Automatica : a journal of IFAC, the International Federation of Automatic Control. - Amsterdam [u.a.] : Elsevier, Pergamon Press, ISSN 00051098, Bd. 82 (2017), S. 243-250
https://doi.org/10.1016/j.automatica.2017.04.038
Müller, Matthias A.; Worthmann, Karl
Quadratic costs do not always work in MPC. - In: Automatica : a journal of IFAC, the International Federation of Automatic Control. - Amsterdam [u.a.] : Elsevier, Pergamon Press, ISSN 00051098, Bd. 82 (2017), S. 269-277
https://doi.org/10.1016/j.automatica.2017.04.058
Fleige, Andreas; Winkler, Henrik
An indefinite inverse spectral problem of Stieltjes type. - In: Integral equations and operator theory : IEOT. - Berlin : Springer, ISSN 14208989, Bd. 87 (2017), 4, S. 491-514
https://doi.org/10.1007/s00020-017-2358-x
Gernandt, Hannes; Trunk, Carsten
Eigenvalue placement for regular matrix pencils with rank one perturbations. - In: SIAM journal on matrix analysis and applications. - Philadelphia, Pa : Soc, ISSN 10957162, Bd. 38 (2017), 1, S. 134-154
http://dx.doi.org/10.1137/16M1066877
Ilchmann, Achim; Reis, Timo
. - Surveys in differential-algebraic equations ; 4. - Cham : Springer. - ix, 305 Seiten. - (Differential-algebraic equations forum)
http://www.gbv.de/dms/ilmenau/toc/884524973.PDF
Jacob, Birgit; Tretter, Christiane; Trunk, Carsten; Vogt, Hendrik
Numerical range and quadratic numerical range for damped systems. - Ilmenau : Technische Universität, Institut für Mathematik. - 1 Online-Ressource (27 Seiten). - (Preprint. - M17,05)

We prove new enclosures for the spectrum of non-selfadjoint operator matrices associated with second order linear differential equations z'' (t) + D z' (t) + A_0 z(t) = 0 in a Hilbert space. Our main tool is the quadratic numerical range for which we establish the spectral inclusion property under weak assumptions on the operators involved; in particular, the damping operator only needs to be accretive and may have the same strength as A_0. By means of the quadratic numerical range, we establish tight spectral estimates in terms of the unbounded operator coefficients A_0 and D which improve earlier results for sectorial and selfadjoint D; in contrast to numerical range bounds, our enclosures may even provide bounded imaginary part of the spectrum or a spectral free vertical strip. An application to small transverse oscillations of a horizontal pipe carrying a steady-state flow of an ideal incompressible fluid illustrates that our new bounds are explicit.


https://www.db-thueringen.de/receive/dbt_mods_00031984
Ilchmann, Achim; Reis, Timo
Outer transfer functions of differential-algebraic systems. - In: Control, optimisation and calculus of variations : COCV. - Les Ulis : EDP Sciences, ISSN 12623377, Bd. 23 (2017), 2, S. 391-425
https://doi.org/10.1051/cocv/2015051
Derkach, Vladimir; Trunk, Carsten
Coupling of definitizable operators in Krein spaces. - Ilmenau : Technische Universität, Institut für Mathematik. - 1 Online-Ressource (18 Seiten). - (Preprint. - M17,03)

Indefinite Sturm-Liouville operators defined on the real line are often considered as a coupling of two semibounded symmetric operators defined on the positive and the negative half axis. In many situations, those two semibounded symmetric operators have in a special sense good properties like a Hilbert space self-adjoint extension. In this paper we present an abstract approach to the coupling of two (definitizable) self-adjoint operators. We obtain a characterization for the definitizability and the regularity of the critical points. Finally we study a typical class of indefinite Sturm-Liouville problems on the real line.


https://www.db-thueringen.de/receive/dbt_mods_00031469
Fleige, Andreas; Winkler, Henrik
An indefinite inverse spectral problem of Stieltjes type. - Ilmenau : Technische Universität, Institut für Mathematik. - 1 Online-Ressource (25 Seiten). - (Preprint. - M17,02)
https://www.db-thueringen.de/receive/dbt_mods_00031460
Giribet, Juan; Langer, Matthias; Leben, Leslie; Maestripieri, Alejandra; Martínez Pería, Francisco; Trunk, Carsten
Spectrum of J-frame operators. - Ilmenau : Technische Universität, Institut für Mathematik. - 1 Online-Ressource (20 Seiten). - (Preprint. - M17,01)

A J-frame is a frame F for a Krein space which is compatible with the indefinite inner product in the sense that it induces an indefinite reconstruction formula that resembles those produced by orthonormal bases in H . With every J-frame the so-called J-frame operator is associated, which is a self-adjoint operator in the Krein space H. The J-frame operator plays an essential role in the indefinite reconstruction formula. In this paper we characterize the class of J-frame operators in a Krein space by a 2X2 block operator representation. The J-frame bounds of F are then recovered as the suprema and infima of the numerical ranges of some uniformly positive operators which are build from the entries of the 2X2 block representation. Moreover, this 2X2 block representation is utilized to obtain enclosures for the spectrum of J-frame operators, which finally leads to the construction of a square root. This square root allows a complete description of all J-frames associated with a given J-frame operator.


https://www.db-thueringen.de/receive/dbt_mods_00031058
Proch, Michael; Worthmann, Karl; Schlüchtermann, Jörg
A negotiation-based algorithm to coordinate supplier development in decentralized supply chains. - In: European journal of operational research : EJOR. - Amsterdam [u.a.] : Elsevier, ISSN 03772217, Bd. 256 (2017), 2, S. 412-429
http://dx.doi.org/10.1016/j.ejor.2016.06.029
Braun, Philipp; Faulwasser, Timm; Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.; Worthmann, Karl
Maximal islanding time for microgrids via distributed predictive control. - In: 22nd International Symposium on Mathematical Theory of Networks and Systems : July 12-15, 2016, University of Minnesota, Twin Cities Campus. - Minneapolis, MN : University Digital Conservancy / International Symposium on Mathematical Theory of Networks and Systems ; 22 (Minneapolis, Minn.) : 2016.07.12-15., ISBN 978-1-5323-1358-5, (2016), S. 652-659

http://hdl.handle.net/11299/181518
Braun, Philipp; Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.; Worthmann, Karl
Model predictive control of residential energy systems using energy storage and controllable loads. - In: Progress in industrial mathematics at ECMI 2014. - Cham : Springer International Publishing / ECMI ; 18 (Taormina) : 2014.06.09-13., ISBN 978-3-319-23413-7, (2016), S. 617-623

https://doi.org/10.1007/978-3-319-23413-7_85
Shkalikov, A. A.; Trunk, Carsten
On stability of closedness and self-adjointness for 2 x 2 operator matrices. - In: Mathematical notes. - Dordrecht [u.a.] : Springer Science + Business Media B.V, ISSN 15738876, Bd. 100 (2016), 5, S. 870-875
http://dx.doi.org/10.1134/S0001434616110274
Braun, Philipp; Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.; Worthmann, Karl
A distributed optimization algorithm for the predictive control of smart grids. - In: IEEE transactions on automatic control. - New York, NY : Institute of Electrical and Electronics Engineers, ISSN 15582523, Bd. 61 (2016), 12, S. 3898-3911
https://doi.org/10.1109/TAC.2016.2525808
Jacob, Birgit; Langer, Matthias; Trunk, Carsten
Variational principles for self-adjoint operator functions arising from second-order systems. - In: Operators and matrices : OaM. - Zagreb : Element, Bd. 10 (2016), 3, S. 501-531
http://dx.doi.org/10.7153/oam-10-29
Behrndt, Jussi; Schmitz, Philipp; Trunk, Carsten
Bounds on the non-real spectrum of a singular indefinite Sturm-Liouville operator on R. - In: Proceedings in applied mathematics and mechanics : PAMM. - Weinheim [u.a.] : Wiley-VCH, ISSN 16177061, Bd. 16 (2016), 1, S. 881-882
http://dx.doi.org/10.1002/pamm.201610429
Gernandt, Hannes; Trunk, Carsten
On the parametric eigenvalue behavior of matrix pencils under rank one perturbations. - In: Proceedings in applied mathematics and mechanics : PAMM. - Weinheim [u.a.] : Wiley-VCH, ISSN 16177061, Bd. 16 (2016), 1, S. 873-874
http://dx.doi.org/10.1002/pamm.201610425
Büttner, Florian; Trunk, Carsten
Limit-point/limit-circle classification of second-order differential operators arising in PT quantum mechanics. - In: Proceedings in applied mathematics and mechanics : PAMM. - Weinheim [u.a.] : Wiley-VCH, ISSN 16177061, Bd. 16 (2016), 1, S. 871-872
http://dx.doi.org/10.1002/pamm.201610424
Škalikov, Andrej Andreevič; Trunk, Carsten
Ob ustojčivosti zamknutosti i samosoprjažennosti dlja 2 x 2 operator-matric. - Ilmenau : Technische Universität, Institut für Mathematik. - 1 Online-Ressource (6 Seiten). - (Preprint. - M16,07)

Consider an operator which is defined in Banach or Hilbert space by a 2x2 matrix with entries A, B, C, D which where linear operators and which are assumed to be unbounded. In the case when the operators C and B are relatively bounded with respect to the operators A and D, respectively, new conditions of the closeness or closability are obtained for the operator L. For the operator L acting in a Hilbert space the analogs of Rellich-Kato theorems on the stability of self-adjointness are obtained.


https://www.db-thueringen.de/receive/dbt_mods_00030580
Ilchmann, Achim
EAGLE-Starthilfe Mathematik und Gesellschaft : zur Funktion der angewandten Mathematik. - Leipzig : Edition am Gutenbergplatz Leipzig. - 97 Seiten. - (Eagle. - 093)
Literaturverzeichnis: Seite 91-94
http://www.gbv.de/dms/ilmenau/toc/868029009.PDF
Leben, Leslie
Non-negative operators in Krein spaces and rank one perturbations. - Ilmenau : Universitätsverlag Ilmenau. - Online-Ressource (PDF-Datei: 116 Seiten, 6.65 MB)
Technische Universität Ilmenau, Dissertation, 2016

In der vorliegenden Arbeit werden eindimensionale Störungen von nichtnegativen Operatoren in Kreinräumen betrachtet. Dabei wird untersucht wie sich die Anzahl der Eigenwerte und deren Vielfachheit in einer Lücke des essentiellen Spektrums unter einer Störung ändern können. Zudem wird beschrieben wie sich an einem Eigenwert die Anzahl und die Länge der linear unabhängigen Jordanketten ändern können.


https://www.db-thueringen.de/receive/dbt_mods_00029981
Worthmann, Karl; Proch, Michael; Braun, Philipp; Schlüchtermann, Jörg; Pannek, Jürgen
Towards dynamic contract extension in supplier development. - In: Logistics research. - Berlin : Springer, ISSN 18650368, Bd. 9Bd. 9.2016, Article 14, S. 1-12
http://hdl.handle.net/10419/157739
Worthmann, Karl; Mehrez, Mohamed W.; Zanon, Mario; Mann, George K. I.; Gosine, Raymond G.; Diehl, Moritz
Model predictive control of nonholonomic mobile robots without stabilizing constraints and costs. - In: IEEE transactions on control systems technology : a publication of the IEEE Control Systems Society. - New York, NY : IEEE, ISSN 15580865, Bd. 24 (2016), 4, S. 1394-1406
http://dx.doi.org/10.1109/TCST.2015.2488589
Büttner, Florian; Trunk, Carsten
Limit-point/limit-circle classification of second-order differential operators arising in PT quantum mechanics. - Ilmenau : Technische Universität, Institut für Mathematik. - 1 Online-Ressource (6 Seiten). - (Preprint. - M16,03)
https://www.db-thueringen.de/receive/dbt_mods_00029270
Behrndt, Jussi; Schmitz, Philipp; Trunk, Carsten
Bounds on the non-real spectrum of a singular indefinite Sturm-Liouville operator on R. - Ilmenau : Technische Universität, Institut für Mathematik. - 1 Online-Ressource (4 Seiten). - (Preprint. - M16,05)

A simple explicit bound on the absolute values of the non-real eigenvalues of a singular indefinite Sturm-Liouville operator on the real line with the weight function sgn(&hahog;) and an integrable, continuous potential q is obtained.


https://www.db-thueringen.de/receive/dbt_mods_00029271
Gernandt, Hannes; Trunk, Carsten
On the parametric eigenvalue behavior of matrix pencils under rank one perturbations. - Ilmenau : Technische Universität, Institut für Mathematik. - 1 Online-Ressource (8 Seiten). - (Preprint. - M16,04)

We study the eigenvalues of rank one perturbations of regular matrix pencils depending linearly on a complex parameter. We prove properties of the corresponding eigenvalue sets including a convergence result as the parameter tends to infinity and an eigenvalue interlacing property for real valued pencils having real eigenvalues only.


https://www.db-thueringen.de/receive/dbt_mods_00029233
Ilchmann, Achim; Selig, Tilman; Trunk, Carsten
The Byrnes-Isidori form for infinite-dimensional systems. - In: SIAM journal on control and optimization. - Philadelphia, Pa : Soc, ISSN 10957138, Bd. 54 (2016), 3, S. 1504-1534
http://dx.doi.org/10.1137/130942413
Behrndt, Jussi; Möws, Roland; Trunk, Carsten
Eigenvalue estimates for operators with finitely many negative squares. - Ilmenau : Technische Universität, Institut für Mathematik. - 1 Online-Ressource (14 Seiten). - (Preprint. - M16,02)

Let A and B be selfadjoint operators in a Krein space. Assume that the re- solvent difference of A and B is of rank one and that the spectrum of A consists in some interval I of isolated eigenvalues only. In the case that A is an operator with finitely many negative squares we prove sharp estimates on the number of eigenvalues of B in the interval I. The general results are applied to singular indefinite Sturm-Liouville problems.


https://www.db-thueringen.de/receive/dbt_mods_00029046
Worthmann, Karl; Braun, Philipp; Proch, Michael; Schlüchtermann, Jörg; Pannek, Jürgen
On contractual periods in supplier development. - In: IFAC-PapersOnLine. - Frankfurt : Elsevier, ISSN 24058963, Bd. 49 (2016), 2, S. 60-65
http://dx.doi.org/10.1016/j.ifacol.2016.03.011
Behrndt, Jussi; Leben, Leslie; Martínez Pería, Francisco; Möws, Roland; Trunk, Carsten
Sharp eigenvalue estimates for rank one perturbations of nonnegative operators in Krein spaces. - In: Journal of mathematical analysis and applications. - Amsterdam [u.a.] : Elsevier, Bd. 439 (2016), 2, S. 864-895
http://dx.doi.org/10.1016/j.jmaa.2016.03.012
Gernandt, Hannes; Trunk, Carsten
Eigenvalue placement for regular matrix pencils with rank one perturbations. - Ilmenau : Technische Universität, Institut für Mathematik. - 1 Online-Ressource (15 Seiten). - (Preprint. - M16,01)

A regular matrix pencil sE-A and its rank one perturbations are considered. We determine the sets in \C\cup\{\infty\} which are the eigenvalues of the perturbed pencil. We show that the largest Jordan chains at each eigenvalue of sE-A may disappear and the sum of the length of all destroyed Jordan chains is the number of eigenvalues (counted with multiplicities) which can be placed arbitrarily in \C\cup\{\infty\}. We prove sharp upper and lower bounds of the change of the algebraic and geometric multiplicity of an eigenvalue under rank one perturbations. Finally we apply our results to a pole placement problem for a single-input differential algebraic equation with feedback.


http://www.db-thueringen.de/servlets/DocumentServlet?id=27311
Knobloch, Jürgen; Vielitz, Martin
Non-conservative perturbations of homoclinic snaking scenarios. - In: Journal of differential equations. - Orlando, Fla : Elsevier, ISSN 10902732, Bd. 260 (2016), 1, S. 517-566
http://dx.doi.org/10.1016/j.jde.2015.09.005
Berger, Thomas; Trunk, Carsten; Winkler, Henrik
Linear relations and the Kronecker canonical form. - In: Linear algebra and its applications : LAA. - New York, NY : American Elsevier Publ, Bd. 488 (2016), S. 13-44
http://dx.doi.org/10.1016/j.laa.2015.09.033
Philipp, Friedrich; Trunk, Carsten
Spectral points of type π+ and type π- of closed operators in indefinite inner product spaces. - In: Operators and matrices : OaM. - Zagreb : Element, Bd. 9 (2015), 3, S. 481-506
Im Titel ist "+" und "-" tiefgestellt
http://dx.doi.org/10.7153/oam-09-30
Braun, Philipp; Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.; Worthmann, Karl
Predictive control of a smart grid: a distributed optimization algorithm with centralized performance properties. - In: 2015 54th IEEE Conference on Decision and Control (CDC) : date: 15-18 Dec. 2015. - [Piscataway, NJ] : IEEE / IEEE Conference on Decision and Control ; 54 (Osaka) : 2015.12.15-18., ISBN 978-1-4799-7886-1, (2015), S. 5593-5598

http://dx.doi.org/10.1109/CDC.2015.7403096
Worthmann, Karl; Mehrez, Mohamed W.; Zanon, Mario; Mann, George K. I.; Gosine, Raymond G.; Diehl, Moritz
Regulation of differential drive robots using continuous time MPC without stabilizing constraints or costs. - In: IFAC-PapersOnLine. - Frankfurt : Elsevier, ISSN 24058963, Bd. 48 (2015), 23, S. 129-135
http://dx.doi.org/10.1016/j.ifacol.2015.11.272
Braun, Philipp; Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.; Worthmann, Karl
A real-time pricing scheme for residential energy systems using a market maker. - In: Proceedings of 2015 Australian Control Conference (AUCC 2015) : Gold Coast, Australia, 05-06 November 2015. - [Piscataway, NJ] : IEEE / Australian Control Conference ; 5 (Gold Coast) : 2015.11.05-06., ISBN 978-1-922107-69-5, (2015), S. 259-262

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7361944
Worthmann, Karl; Reble, Marcus; Grüne, Lars; Allgöwer, Frank
Unconstrained nonlinear MPC: performance estimates for sampled-data systems with zero order hold. - In: 2015 54th IEEE Conference on Decision and Control (CDC) : date: 15-18 Dec. 2015. - [Piscataway, NJ] : IEEE / IEEE Conference on Decision and Control ; 54 (Osaka) : 2015.12.15-18., ISBN 978-1-4799-7886-1, (2015), S. 4971-4976

http://dx.doi.org/10.1109/CDC.2015.7402996
Ilchmann, Achim; Reis, Timo
. - Surveys in differential-algebraic equations ; 3. - Cham [u.a.] : Springer. - IX, 313 S.. - (Differential-algebraic equations forum, DAE-F)
Literaturangaben
http://www.gbv.de/dms/ilmenau/toc/839330669.PDF
Selig, Tilman
On output feedback control of infinite-dimensional systems. - Online-Ressource (PDF-Datei: IV, 218 S., 1,06 MB)
Ilmenau : Techn. Univ., Diss., 2015

Diese Dissertation behandelt zeitinvariante, unendlichdimensionale, lineare Systeme, die ein Eingangssignal u in ein Ausgangssignal y umwandeln. In der Theorie der kompatiblen, wohlgestellten, linearen Systeme, werden solche Umwandlungen durch Differenzialgleichungen der Formx'(t)=Ax(t)+ Bu(t), y(t)=Cx(t)+Du(t) beschrieben, wobei A, B, C und D lineare Operatoren zwischen Hilbert-Räumen sind, die auch unstetig sein können. Um die Struktur solcher Systeme zu verstehen, werden verschiedene Arten von Zustandsraumtransformationen, die aus der endlichdimensionalen Theorie bekannt sind verallgemeintert: Für Systeme mit kompaktem Hankel-Operator werden ausgangsnormalisierende sowie balancierende Transformationen konstruiert und für die Modellreduktion eingesetzt. Für Systeme mit natürlichzahligem Relativgrad werden Transformationen entwickelt um die Byrnes-Isidori-Form und eine verwandte, sogenannte Nulldynamikform zu verallgemeinern. Darüberhinaus wird die Nulldynamik für unendlichdimensionaly Systeme erstmals rigoros definitiert und gezeigt, dass sie bei Systemen mit natürlichzahligem Relativgrad durch eine einzige stark stetige Operatorhalbgruppe charakterisiert werden kann. Dazu wird die Nulldynamikform verwendet. Ein analoges Resultat wird für ein spezielles Randsteuerungsproblem bewiesen, dass durch eine Wärmeleitungsgleichung beschrieben wird. Im Anschluss an diese theoretischen Überlegungen wird bewiesen, dass zwei praktische einsetzbare Ausgangsrückführungsmethode funktionieren: Die erste Methode ist die sogenannte Funnelregelung, ein sehr einfaches Regelgesetz, welches der Trajektorienverfolgung dient. Es wird gezeigt, dass diese Methode efolgreich einsetzbar ist sowohl bei Systemen mit Relativgrad eins und exponenziell stabiler Nulldynamik, als auch bei dem erwähnten speziellen Randsteuerungsproblem.Die zweite Ausgangsrückführung, die untersucht wird dient der Störgrößenunterdrückung. Es ist eine spezielle Form der H-unendlich-Regelung und eng verknüpft oft mit linear-quadratischer Optimalsteuerung. Während die klassische Lösung dieses wohlbekannten Problems stets einen unendlichdimensionalen Beobachter benötigt, der nicht praktisch implementiert werden kann, wird hier ein endlichdimensionaler Regler konstruiert durch balanciertes Abschneiden. Darüberhinaus wird bewiesen, dass dieser praktisch einsetzbare Regler das Regelziel mit einer Regelgüte erreicht, die vom Approxmationsfehler der Modellreduktion abhängt.


http://www.db-thueringen.de/servlets/DocumentServlet?id=26328
Winkler, Henrik
Two-dimensional Hamiltonian systems. - In: Operator theory - Basel ; Heidelberg [u.a.] : Springer Reference, (2015), S. 525-547
Trunk, Carsten
Locally definitizable operators: the local structure of the spectrum. - In: Operator theory - Basel ; Heidelberg [u.a.] : Springer Reference, (2015), S. 241-259
Reis, Timo; Selig, Tilman
Zero dynamics and root locus for a boundary controlled heat equation. - In: Mathematics of control, signals, and systems : MCSS. - London : Springer, ISSN 1435568X, Bd. 27 (2015), 3, S. 347-373
http://dx.doi.org/10.1007/s00498-015-0143-4
Berger, Thomas; Trunk, Carsten; Winkler, Henrik
Linear relations and the Kronecker canonical form. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 27 S., 402 KB). - (Preprint. - M15,05)

We show that the Kronecker canonical form (which is a canonical decomposition for pairs of matrices) is the representation of a linear relation in a finite dimensional space. This provides a new geometric view upon the Kronecker canonical form. Each of the four entries of the Kronecker canonical form has a natural meaning for the linear relation which it represents. These four entries represent the Jordan chains at finite eigenvalues, the Jordan chains at infinity, the so-called singular chains and the multi-shift part. Or, to state it more concise: For linear relations the Kronecker canonical form is the analogue of the Jordan canonical form for matrices.


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Berger, Thomas; Ilchmann, Achim; Wirth, Fabian
Zero dynamics and stabilization for analytic linear systems. - In: Acta applicandae mathematicae : an international survey journal on applying mathematics and mathematical applications. - [S.l.] : Proquest, ISSN 15729036, Bd. 138 (2015), 1, S. 17-57
http://dx.doi.org/10.1007/s10440-014-9956-2
Worthmann, Karl; Kellett, Christopher M.; Braun, Philipp; Grüne, Lars; Weller, Steven R.
Distributed and decentralized control of residential energy systems incorporating battery storage. - In: IEEE transactions on smart grid. - New York, NY : IEEE, Bd. 6 (2015), 4, S. 1914-1923
http://dx.doi.org/10.1109/TSG.2015.2392081
Reis, Timo; Selig, Tilman
Funnel control for the boundary controlled heat equation. - In: SIAM journal on control and optimization. - Philadelphia, Pa : Soc, ISSN 10957138, Bd. 53 (2015), 1, S. 547-574
http://dx.doi.org/10.1137/140971567
Behrndt, Jussi; Leben, Leslie; Martínez Pería, Francisco; Trunk, Carsten
The effect of finite rank perturbations on Jordan chains of linear operators. - In: Linear algebra and its applications : LAA. - New York, NY : American Elsevier Publ, Bd. 479 (2015), S. 118-130
http://dx.doi.org/10.1016/j.laa.2015.04.007
Ilchmann, Achim; Reis, Timo
. - Surveys in differential-algebraic equations ; 2. - Cham [u.a.] : Springer. - VII, 339 S.. - (Differential-algebraic equations forum, DAE-F)
Literaturangaben
http://www.gbv.de/dms/ilmenau/toc/819604070.PDF
Selig, Tilman
Controller reduction by H∞ balanced truncation for infinite-dimensional, discrete-time systems. - In: Mathematics of control, signals, and systems : MCSS. - London : Springer, ISSN 1435568X, Bd. 27 (2015), 1, S. 111-147
http://dx.doi.org/10.1007/s00498-014-0137-7
Ilchmann, Achim
Zur gesellschaftlichen Funktion der angewandten Mathematik. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 31 S., 396 KB). - (Preprint. - M15,02)

Der Begriff derWissenschaft wird expliziert; die Einzelwissenschaften Philosophie, Natur und Technikwissenschaften und Mathematik werden historisch und systematisch eingeordnet, um insbesondere den Unterschied zwischen Technologie und angewandter Mathematik zu verstehen. Es wird dann Peter Bulthaups These der "tendenziellen Transformation von Wissenschaft in Technologie" für die angewandte Mathematik untersucht.


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Reis, Timo; Selig, Tilman
Funnel control for the boundary controlled heat equation. - Hamburg : Fachbereich Mathematik, Universität Hamburg. - 1 Online-Ressource (33 Seiten, 264 MB). - (Hamburger Beiträge zur Angewandten Mathematik. - 2014,13)
http://edok01.tib.uni-hannover.de/edoks/e01fn16/866296891.pdf
Berger, Thomas; Ilchmann, Achim; Reis, Timo
Funnel control for nonlinear functional differential-algebraic systems. - In: MTNS 2014 / International Symposium on Mathematical Theory of Networks and Systems ; 21 (Groningen) : 2014.07.07-11. - Groningen : Univ. of Groningen, ISBN 978-90-367-6321-9, 2014, Paper MoA02.4, insges. 7 S.

Boccia, Andrea; Grüne, Lars; Worthmann, Karl
Stability and feasibility of state-constrained linear MPC without stabilizing terminal constraints. - In: MTNS 2014 / International Symposium on Mathematical Theory of Networks and Systems ; 21 (Groningen) : 2014.07.07-11. - Groningen : Univ. of Groningen, ISBN 978-90-367-6321-9, 2014, Paper TuA07.4, insges. 8 S.

Vielitz, Martin
Nonreversible homoclinic snaking scenarios. - Online-Ressource (PDF-Datei: III, 139 S., 2,63 MB)
Ilmenau : Techn. Univ., Diss., 2014

Homoclinic Snaking ist ein spezielles Phänomen bei der Fortsetzung homokliner Orbits in der Nähe eines heteroklinen Zykels, welcher eine Gleichgewichtslage und einen periodischen Orbit verbindet. Der Begriff "Snaking" bezieht sich dabei auf die Sinusform der Fortsetzungskurven. Typischer Weise tritt dieses Phänomen in reversiblen Hamilton-Systemen auf. Dabei entsprechen die zwei Snaking-Kurven symmetrischen Homoklinen, wohingegen asymmetrische Homoklinen auf Kurvenstücken liegen, welche die beiden Snaking-Kurven verbinden. Zusammengenommen bilden die Fortsetzungskurven die Snakes-and-ladders Struktur. In dieser Arbeit wird Homoclinic Snaking in nichtreversiblen DGLs betrachtet, deren reversible Struktur (allein oder zusammen mit der Hamilton Struktur) gestört wird. Ausgangspunkt dafür ist die Arbeit von Beck et. al. (Snakes, ladders, and isolas of localised patterns). Es wird gezeigt, dass die Störung der Reversibilität geschlossene Fortsetzungskurven (Isolas) oder zwei Fortsetzungskurven, hervorrufen kann, welche alternierend den ursprünglichen sinusförmigen Fortsetzungskurven (Criss-Cross Snaking) folgen. Darüber hinaus wird Homoclinic Snaking in gewöhnlichen DGLs betrachtet, welche von Beginn an keine ausgezeichnete Struktur besitzen. Es wird untersucht, wie das Verhalten des ursprünglichen heteroklinen Zykels das Fortsetzungsverhalten bestimmt. Dabei werden die beiden Fälle unterschieden, dass der periodische Orbit positive oder negative Floquet Multiplikatoren besitzt. Des Weiteren wird ein Fortsetzungsszenario bestehend aus Isolas beschrieben. Weiterhin werden Fenichelkoordinaten in der Nähe einer 1-parametrigen Familie von periodischen Orbits, in welcher in sich die Dimension der stabilen Mannigfaltigkeit ändert, konstruiert. Dazu wird eine Foliation einer erweiterten stabilen Mannigfaltigkeit konstruiert. Es wird gezeigt, dass wenn der schwach stabile Floquet Exponent gegen Null strebt, die Foliation auch im Grenzwert glatt ist. Darüber hinaus wird ein Shilnikov Problem in der Nähe der 1-parametrigen Familie von periodischen Orbits gelöst, wenn der schwach stabile Floquet Exponent gegen Null strebt. Die Analysis basiert auf der Arbeit von Krupa et al. (Fast and slow waves in the FitzHugh-Nagumo equation).


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Worthmann, Karl; Kellett, Christopher M.; Grüne, Lars; Weller, Steven
Distributed control of residential energy systems using a market maker. - In: 19th IFAC world congress 2014 / IFAC world congress ; 19 (Cape Town) : 2014.08.24-29. - Red Hook, NY : Curran, (2014), S. 11641-11646
Azizov, Tomas Ya.; Trunk, Carsten
On a class of Sturm-Liouville operators which are connected to PT symmetric problems. - In: Proceedings in applied mathematics and mechanics : PAMM. - Weinheim [u.a.] : Wiley-VCH, ISSN 16177061, Bd. 14 (2014), 1, S. 991-992
http://dx.doi.org/10.1002/pamm.201410476
Worthmann, Karl; Reble, Marcus; Grüne, Lars; Allgöwer, Frank
Nonlinear MPC: the impact of sampling on closed loop stability. - In: Proceedings in applied mathematics and mechanics : PAMM. - Weinheim [u.a.] : Wiley-VCH, ISSN 16177061, Bd. 14 (2014), 1, S. 911-912
http://dx.doi.org/10.1002/pamm.201410436
Winkler, Henrik; Woracek, Harald
A growth condition for Hamiltonian systems related with Krein strings. - In: Acta scientiarum mathematicarum. - Szeged, Bd. 80 (2014), 1/2, S. 31-94
http://dx.doi.org/10.14232/actasm-012-028-8
Huang, Junjie; Sun, Junfeng; Chen, Alatancang; Trunk, Carsten
The invertibility of 2 x 2 operator matrices. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 19 S., 305 KB). - (Preprint. - M14,10)

In this paper the properties of right invertible row operators, i.e., of 1x2 surjective operator matrices are studied. This investigation is based on a specific space decomposition. Using this decomposition, we characterize the invertibility of a 2x2 operator matrix. As an application, the invertibility of Hamiltonian operator matrices is investigated.


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Jacob, Birgit; Langer, Matthias; Trunk, Carsten
Variational principles for self-adjoint operator functions arising from second-order systems. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 30 S., 455 KB). - (Preprint. - M14,09)
http://www.db-thueringen.de/servlets/DocumentServlet?id=25046
Boccia, Andrea; Grüne, Lars; Worthmann, Karl
Stability and feasibility of state constrained MPC without stabilizing terminal constraints. - In: Systems & control letters. - Amsterdam [u.a.] : Elsevier, ISSN 18727956, Bd. 72 (2014), S. 14-21
http://dx.doi.org/10.1016/j.sysconle.2014.08.002
Ilchmann, Achim; Reis, Timo
Outer transfer functions of differential-algebraic systems. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 39 S., 403,1 KB). - (Preprint. - M14,07)

We consider differential-algebraic systems whose transfer function is outer: i.e., it has full row rank and all transmission zeros lie in the closed left half complex plane. We characterize outer, with the aid of the Kronecker structure of the system pencil and the Smith-McMillan structure of the transfer function, as the following property of a behavioural stabilizable and detectable realization: each consistent initial value can be asymptotically controlled to zero while the output can be made arbitrarily small in the L2-norm. The zero dynamics of systems with outer transfer functions are analyzed. We further show that our characterizations of outer provide a simple and very structured analysis of the linear-quadratic optimal control problem.


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Knobloch, Jürgen; Lamb, Jeroen S. W.; Webster, Kevin N.
Using Lin's method to solve Bykov's problems. - In: Journal of differential equations. - Orlando, Fla : Elsevier, ISSN 10902732, Bd. 257 (2014), 8, S. 2984-3047
http://dx.doi.org/10.1016/j.jde.2014.06.006
Snoo, Henk; Fleige, Andreas; Hassi, Seppo; Winkler, Henrik
Non-semi-bounded closed symmetric forms associated with a generalized Friedrichs extension. - In: Proceedings / A. - Cambridge [u.a.] : Cambridge Univ. Press, ISSN 14737124, Bd. 144 (2014), 4, S. 731-745
http://dx.doi.org/10.1017/S0308210512000108
Reis, Timo; Selig, Tilman
Zero dynamics and root locus for a boundary controlled heat equation. - Hamburg : Fachbereich Mathematik, Univ. Hamburg. - Online-Ressource (PDF-Datei: 29 S., 229 KB). - (Hamburger Beiträge zur Angewandten Mathematik. - 2014,08)
http://edok01.tib.uni-hannover.de/edoks/e01fn14/788546341.pdf
Worthmann, Karl; Damm, Tobias; Grüne, Lars; Stieler, Marleen
An exponential turnpike theorem for dissipative discrete time optimal control problems. - In: SIAM journal on control and optimization. - Philadelphia, Pa : Soc, ISSN 10957138, Bd. 52 (2014), 3, S. 1935-1957
http://dx.doi.org/10.1137/120888934
Worthmann, Karl; Reble, Marcus; Grüne, Lars; Allgöwer, Frank
The role of sampling for stability and performance in unconstrained nonlinear model predictive control. - In: SIAM journal on control and optimization. - Philadelphia, Pa : Soc, ISSN 10957138, Bd. 52 (2014), 1, S. 581-605
http://dx.doi.org/10.1137/12086652X
Philipp, Friedrich; Trunk, Carsten
Spectral points of type π + and type π - of closed operators in indefinite inner product spaces. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 27 S., 218 KB). - (Preprint. - M14,04)

We introduce the notion of spectral points of type π+ and type π- of closed operators A in a Hilbert space which is equipped with an indefinite inner product. It is shown that these points are stable under compact perturbations. In the second part of the paper we assume that A is symmetric with respect to the indefinite inner product and prove that the growth of the resolvent of A is of finite order in a neighborhood of a real spectral point of type π+ or π- which is not in the interior of the spectrum of A. Finally, we prove that there exists a local spectral function on intervals of type π+ or π-.


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Reis, Timo; Selig, Tilman
Balancing transformations for infinite-dimensional systems with nuclear Hankel operator. - In: Integral equations and operator theory : IEOT. - Berlin : Springer, ISSN 14208989, Bd. 79 (2014), 1, S. 67-105
http://dx.doi.org/10.1007/s00020-013-2105-x
Behrndt, Jussi; Leben, Leslie; Philipp, Friedrich
Variation of discrete spectra of non-negative operators in Krein spaces. - In: Journal of operator theory. - Bucharest, ISSN 18417744, Bd. 71 (2014), 1, S. 157-173
http://dx.doi.org/10.7900/jot.2011nov30.1964
Azizov, Tomas Ya.; Trunk, Carsten
On limit point and limit circle classification for PT symmetric operators. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 5 S., 103,3 KB). - (Preprint. - M14,03)

A prominent class of PT-symmetric Hamiltonians is $H:= 1/2 p^2 + x^2 (ix)^N, for x \in \Gamma$ for some nonnegative number N. The associated eigenvalue problem is defined on a contour $\Gamma$ in a specific area in the complex plane (Stokes wedges), see [3,5]. In this short note we consider the case N=2 only. Here we elaborate the relationship between Stokes lines and Stokes wedges and well-known limit point/limit circle criteria from [11, 6, 10].


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Behrndt, Jussi; Leben, Leslie; Martínez Pería, Francisco; Trunk, Carsten
The effect of finite rank perturbations on Jordan chains of linear operators. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 12 S., 280,7 KB). - (Preprint. - M14,02)

A general result on the structure and dimension of the root subspaces of a matrix or a linear operator under finite rank perturbations is proved: The increase of dimension from the n-th power of the kernel of the perturbed operator to the (n+1)-th power differs from the increase of dimension of the corresponding powers of the kernels of the unperturbed operator by at most the rank of the perturbation and this bound is sharp.


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Behrndt, Jussi; Möws, Roland; Trunk, Carsten
On finite rank perturbations of selfadjoint operators in Krein spaces and eigenvalues in spectral gaps. - In: Complex analysis and operator theory. - Cham (ZG) : Springer International Publishing AG, ISSN 16618262, Bd. 8 (2014), 4, S. 925-936
http://dx.doi.org/10.1007/s11785-013-0318-2
Snoo, Henk; Winkler, Henrik; Wojtylak, Michal
Global and local behavior of zeros of nonpositive type. - In: Journal of mathematical analysis and applications. - Amsterdam [u.a.] : Elsevier, Bd. 414 (2014), 1, S. 273-284
http://dx.doi.org/10.1016/j.jmaa.2014.01.004
Pannek, Jürgen; Worthmann, Karl
Stability and performance guarantees for model predictive control algorithms without terminal constraints. - In: ZAMM : journal of applied mathematics and mechanics. - Berlin : Wiley-VCH, ISSN 15214001, Bd. 94 (2014), 4, S. 317-330
http://dx.doi.org/10.1002/zamm.201100133
Homburg, Ale Jan; Kellner, Maria; Knobloch, Jürgen
Construction of codimension one homoclinic cycles. - In: Dynamical systems : an international journal. - London : Taylor & Francis, ISSN 14689375, Bd. 29 (2014), 1, S. 133-151
http://dx.doi.org/10.1080/14689367.2013.860085
Grüne, Lars; Allgöwer, Frank; Findeisen, Rolf; Fischer, Jörg; Groß, Dominik; Hanebeck, Uwe D.; Kern, Benjamin; Müller, Matthias A.; Pannek, Jürgen; Reble, Marcus
Distributed and networked model predictive control. - In: Control theory of digitally networked dynamic systems : . - Cham [u.a.] : Springer, ISBN 978-3-319-01130-1, (2014), S. 111-167

Berger, Thomas
On differential-algebraic control systems. - Ilmenau : Univ.-Verl. Ilmenau. - Online-Ressource (PDF-Datei: 329 S., 1,84 MB)
Zugl.: Ilmenau : Techn. Univ., Diss., 2013
Unterschiede zwischen dem gedruckten Dokument und der elektronischen Ressource können nicht ausgeschlossen werden

In der vorliegenden Dissertation werden differential-algebraische Gleichungen (differential-algebraic equations, DAEs) der Form d dt Ex = Ax + f betrachtet, wobei E und A beliebige Matrizen sind. Falls E nichtverschwindende Einträge haben, dann kommen in der Gleichung Ableitungen der entsprechenden Komponenten von x vor. Falls E eine Nullzeile hat, dann kommen in der entsprechenden Gleichung keine Ableitungen vor und sie ist rein algebraisch. Daher werden Gleichungen vom Typ d dt Ex = Ax + f differential-algebraische Gleichungen genannt. Ein Ziel dieser Dissertation ist es, eine strukturelle Zerlegung einer DAE in vier Teile herzuleiten: einen ODE-Anteil, einen nilpotenten Anteil, einen unterbestimmten Anteil und einen überbestimmten Anteil. Jeder Anteil beschreibt ein anderes Lösungsverhalten in Hinblick auf Existenz und Eindeutigkeit von Lösungen für eine vorgegebene Inhomogenität f und Konsistenzbedingungen an f. Die Zerlegung, namentlich die quasi-Kronecker Form (QKF), verallgemeinert die wohlbekannte Kronecker-Normalform und behebt einige ihrer Nachteile. Die QKF wird ausgenutzt, um verschiedene Konzepte der Kontrollierbarkeit und Stabilisierbarkeit für DAEs mit f = Bu zu studieren. Hier bezeichnet u den Eingang des differential-algebraischen Systems. Es werden Zerlegungen unter System- und Feedback-Äquivalenz, sowie die Folgen einer Behavioral-Steuerung K_x x + K_u u = 0 für die Stabilisierung des Systems untersucht. Falls für das DAE-System zusätzlich eine Ausgangs-Gleichung y =Cx gegeben ist, dann lässt sich das Konzept der Nulldynamik wie folgt definieren: die Nulldynamik ist, grob gesagt, die Dynamik, die am Ausgang nicht sichtbar ist, d.h. die Menge aller Lösungs-Trajektorien (x,u,y) mit y = 0. Für rechts-invertierbare Systeme mit autonomer Nulldynamik wird eine Zerlegung hergeleitet, welche die Nulldynamik entkoppelt. Diese versetzt uns in die Lage, eine Behavior-Steuerung zu entwickeln, die das System stabilisiert, vorausgesetzt die Nulldynamik selbst ist stabil. Wir betrachten auch zwei Regelungs-Strategien, die von den Eigenschaften der oben genannten System-Klasse profitieren: Hochverstärkungs- und Funnel-Regelung. Ein System d dt Ex = Ax + Bu, y =Cx, hat die Hochverstärkungseigenschaft, wenn es durch die Anwendung der proportionalen Ausgangsrückführung u = -ky, mit k > 0 hinreichend groß, stabilisiert werden kann. Wir beweisen, dass rechts-invertierbare Systeme mit asymptotisch stabiler Nulldynamik, die eine bestimmte Relativgrad-Annahme erfüllen, die Hochverstärkungseigenschaft haben. Während der Hochverstärkungs-Regler recht einfach ist, ist es jedoch a priori nicht bekannt, wie groß die Verstärkungskonstante k gewählt werden muss. Dieses Problem wird durch den Funnel-Regler gelöst: durch die adaptive Justierung der Verstärkung über eine zeitabhängige Funktion k(.) und die Ausnutzung der Hochverstärkungseigenschaft wird erreicht, dass große Werte k(t) nur dann angenommen werden, wenn sie nötig sind. Eine weitere wesentliche Eigenschaft ist, dass der Funnel-Regler das transiente Verhalten des Fehlers e = y - y ref der Bahnverfolgung, wobei y ref die Referenztrajektorie ist, beachtet. Für einen vordefinierten Performanz-Trichter (funnel) [Psi] wird erreicht, dass e(t) < [Psi](t). Schließlich wird der Funnel-Regler auf die Klasse von MNA-Modellen von passiven elektrischen Schaltkreisen mit asymptotisch stabilen invarianten Nullstellen angewendet. Dies erfordert die Einschränkung der Menge der zulässigen Referenztrajektorien auf solche die, in gewisser Weise, die Kirchhoffschen Gesetze punktweise erfüllen.


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Berger, Thomas; Ilchmann, Achim
On stability of time-varying linear differential-algebraic equations. - In: International journal of control. - London : Taylor & Francis, ISSN 13665820, Bd. 86 (2013), 6, S. 1060-1076
http://dx.doi.org/10.1080/00207179.2013.773087
Berger, Thomas; Ilchmann, Achim; Reis, Timo
Funnel control for nonlinear functional differential-algebraic systems. - Hamburg : Fachbereich Mathematik, Univ. Hamburg. - Online-Ressource (PDF-Datei: 9 S., 131 KB). - (Hamburger Beiträge zur Angewandten Mathematik. - 2013,14)
http://edok01.tib.uni-hannover.de/edoks/e01fn14/788514199.pdf
Reis, Timo; Selig, Tilman
Balancing transformations for infinite-dimensional systems with nuclear Hankel operator. - Hamburg : Univ., Fachbereich Mathematik. - Online-Ressource (PDF-Datei: 41 S., 395 KB). - (Hamburger Beiträge zur Angewandten Mathematik. - 2013,08)
http://edok01.tib.uni-hannover.de/edoks/e01fn14/788498118.pdf
Berger, Thomas; Ilchmann, Achim
On the standard canonical form of time-varying linear DAEs. - In: Quarterly of applied mathematics. - Providence, RI : Brown University, Division of Applied Mathematics, ISSN 15524485, Bd. 71 (2013), 1, S. 69-87
http://dx.doi.org/10.1090/S0033-569X-2012-01285-1
Berger, Thomas; Trenn, Stephan
Addition to "the quasi-Kronecker form for matrix pencils". - In: SIAM journal on matrix analysis and applications. - Philadelphia, Pa : Soc, ISSN 10957162, Bd. 34 (2013), 1, S. 94-101
http://dx.doi.org/10.1137/120883244
Hackl, Christoph M.; Hopfe, Norman; Ilchmann, Achim; Mueller, Markus; Trenn, Stephan
Funnel control for systems with relative degree two. - In: SIAM journal on control and optimization. - Philadelphia, Pa : Soc, ISSN 10957138, Bd. 51 (2013), 2, S. 965-995
http://dx.doi.org/10.1137/100799903
Ilchmann, Achim; Wirth, Fabian
On minimum phase. - In: Automatisierungstechnik : AT. - Berlin : De Gruyter, ISSN 01782312, Bd. 61 (2013), 12, S. 805-817
http://dx.doi.org/10.1524/auto.2013.1002
Reis, Timo; Selig, Tilman
Balancing transformations for infinite-dimensional control systems. - In: Proceedings in applied mathematics and mechanics : PAMM. - Weinheim [u.a.] : Wiley-VCH, ISSN 16177061, Bd. 13 (2013), 1, S. 465-466
http://dx.doi.org/10.1002/pamm.201310225
Berger, Thomas
Funnel control for linear DAEs. - In: Proceedings in applied mathematics and mechanics : PAMM. - Weinheim [u.a.] : Wiley-VCH, ISSN 16177061, Bd. 13 (2013), 1, S. 463-464
http://dx.doi.org/10.1002/pamm.201310224
Fleige, Andreas; Hassi, Seppo; Snoo, Henk; Winkler, Henrik
Non-semibounded closed symmetric forms associated with a generalized Friedrichs extension. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 14 S., 407 KB). - (Preprint. - M13,17)
http://www.db-thueringen.de/servlets/DocumentServlet?id=23178
Winkler, Henrik; Woracek, Harald
A growth condition for Hamiltonian systems related with Krein strings. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 55 S., 732,2 KB). - (Preprint. - M13,16)
http://www.db-thueringen.de/servlets/DocumentServlet?id=23176
Winkler, Henrik
Two-dimensional Hamiltonian systems. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 19 S., 411 KB). - (Preprint. - M13,15)
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Ilchmann, Achim; Selig, Tilman; Trunk, Carsten
The Byrnes-Isidori form for infinite-dimensional systems. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 28 S., 470,8 KB). - (Preprint. - M13,14)

We define a Byrnes-Isidori form for a class of infinite-dimensional systems with relative degree r and show that any system belonging to this class can be transformed into this form. We also analyze the concept of (stable) zero dynamics and show that it is, together with the Byrnes-Isidori form, instrumental for static proportional high-gain output feedback stabilization. Moreover, we show that funnel control is feasible for any system with relative degree one and with exponentially stable zero dynamics; a funnel controller is a time-varying proportional output feedback controller which ensures, for a large class of reference signals, that the error between the output and the reference signal evolves within a prespecified funnel. Therefore transient behavior of the error is obeyed.


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Behrndt, Jussi; Leben, Leslie; Martínez Pería, Francisco; Möws, Roland; Trunk, Carsten
Sharp eigenvalue estimates for rank one perturbations of nonnegative operators in Krein spaces. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 32 S., 308 KB). - (Preprint. - M13,13)

Let A and B be selfadjoint operators in a Krein space and assume that the resolvent difference of A and B is of rank one. In the case that A is nonnegative and I is an open interval such that the spectrum of A in I consists of isolated eigenvalues we prove sharp estimates on the numbers and multiplicities of eigenvalues of B in I. The general result is illustrated with eigenvalue estimates for singular left definite Sturm-Liouville differential operators.


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Trunk, Carsten
Locally definitizable operators: the local structure of the spectrum. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 16 S., 231 KB). - (Preprint. - M13,12)

We consider different types of spectral points of locally definitizable operators which can be defined with the help of approximate eigensequences. Their behavior allow a characterization in terms of the (local) spectral function. Moreover, we review some perturbation results for locally definitizable operators.


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Anderson, Brian D. O.; Ilchmann, Achim; Wirth, Fabian R.
Stabilizability of linear time-varying systems. - In: Systems & control letters. - Amsterdam [u.a.] : Elsevier, ISSN 18727956, Bd. 62 (2013), 9, S. 747-755
http://dx.doi.org/10.1016/j.sysconle.2013.05.003
Behrndt, Jussi; Philipp, Friedrich; Trunk, Carsten
Bounds on the non-real spectrum of differential operators with indefinite weights. - In: Mathematische Annalen. - Berlin : Springer, ISSN 14321807, Bd. 357 (2013), 1, S. 185-213
http://dx.doi.org/10.1007/s00208-013-0904-7
Berger, Thomas; Ilchmann, Achim; Wirth, Fabian R.
Zero dynamics and stabilization for analytic linear systems. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 35 S., 396 KB). - (Preprint. - M13,11)

The feedback stabilization problem is studied for time-varying real analytic systems. We investigate structural properties of the zero dynamics in terms of a system operator over a skew polynomial ring. The concept of (A,B)-invariant time-varying subspaces included in the kernel of C is used to obtain a condition for stabilizability. This condition is equivalent to autonomy of the zero dynamics in case of time-invariant systems. We derive a zero dynamics form for systems which satisfy an assumption close to autonomous zero dynamics; this in some sense resembles the Byrnes-Isidori form for systems with strict relative degree. Some aspects of the latter are also proved. Finally, we show for square systems with autonomous zero dynamics that there exists a linear state feedback such that the Lyapunov exponent of the closed-loop system equals the Lyapunov exponent of the zero dynamics; some boundedness conditions are required, too. If the zero dynamics are exponentially stable this implies that the system can be exponentially stabilized. These results are to some extent also new for time-invariant systems.


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Möws, Roland
Spektrallücken von indefiniten Sturm-Liouville-Operatoren. - Online-Ressource (PDF-Datei: XI, 67 S., 820,4 KB)
Ilmenau : Techn. Univ., Diss., 2013
Unterschiede zwischen dem gedruckten Dokument und der elektronischen Ressource können nicht ausgeschlossen werden

In der Dissertationsschrift "Spektrallücken von indefiniten Sturm-Liouville-Operatoren" werden verschiedene Klassen von selbstadjungierten Operatoren und Relationen in indefiniten Innenprodukträumen betrachtet. Die Arbeit enthält zwei Hauptergebnisse: (A) Für lokal definisierbare Relationen wird gezeigt, dass die Endlichkeit der Anzahl der Eigenwerte in einer reellen Spektrallücke des essentiellen Spektrums unter endlichdimensionalen Störungen erhalten bleibt. (B) Für eine Unterklasse der lokal definisierbare Relationen, nämlich für Relationen mit endlich vielen negativen Quadraten, werden die Anzahl der Eigenwerte der gestörten Relation in einer reellen Spektrallücke des essentiellen Spektrums nach oben/unten durch die Anzahl der Eigenwerte derungestörten Relation und weiteren Korrekturgrößen abgeschätzt. Dabei werden hier nur eindimensionale Störungen betrachtet. Zudem gelingt der Nachweis, dass die in dieser Promotionsschrift vorgestellten Abschätzungen scharf sind.Diese abstrakten Ergebnisse aus dem ersten Teil der Arbeit werden im zweiten Teil auf Sturm-Liouville-Differentialoperatoren mit einer indefinitenGewichtsfunktion angewandt. In vielen Fällen werden die Abschätzungen leicht verbessert.


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Winkler, Henrik; Woracek, Harald
Symmetry in de Branges almost Pontryagin spaces. - In: Integral equations and operator theory : IEOT. - Berlin : Springer, ISSN 14208989, Bd. 76 (2013), 2, S. 179-212
http://dx.doi.org/10.1007/s00020-013-2051-7
Berger, Thomas
Zero dynamics and stabilization for linear DAEs. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 19 S., 140 KB). - (Preprint. - M13,08)
http://www.db-thueringen.de/servlets/DocumentServlet?id=22328
Berger, Thomas; Reis, Timo
Controllability of linear differential-algebraic systems - a survey. - In: Surveys in differential-algebraic equations : . - Berlin [u.a.] : Springer, ISBN 978-3-642-34927-0, (2013), S. 1-61

Berger, Thomas; Reis, Timo
Zero dynamics and funnel control for linear electrical circuits. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 25 S., 217,2 KB). - (Preprint. - M13,07)
http://www.db-thueringen.de/servlets/DocumentServlet?id=22165
Behrndt, Jussi; Hassi, Seppo; Snoo, Henk; Wietsma, Rudi; Winkler, Henrik
Linear fractional transformations of Nevanlinna functions associated with a nonnegative operator. - In: Complex analysis and operator theory. - Cham (ZG) : Springer International Publishing AG, ISSN 16618262, Bd. 7 (2013), 2, S. 331-362
http://dx.doi.org/10.1007/s11785-011-0197-3
Winkler, Henrik; Woracek, Harald
Symmetry in de Branges almost Pontryagin spaces. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 33 S., 303,1 KB). - (Preprint. - M13,06)

In many examples of de Branges spaces symmetry appears naturally. Presence of symmetry gives rise to a decomposition of the space into two parts, the "even" and the "odd" part, which themselves can be regarded as de Branges spaces. The converse question is to decide whether a given space is the "even" part or the "odd" part of some symmetric space, and, if yes, to describe the totality of all such symmetric spaces. We consider this question in an indefinite (almost Pontryagin space) setting, and give a complete answer. Interestingly, it turns out that the answers for the "even" and "odd" cases read quite differently; the latter is significantly more complex.


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Berger, Thomas
Zero dynamics and funnel control of general linear differential-algebraic systems. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 44 S., 438 KB). - (Preprint. - M13,04)
http://www.db-thueringen.de/servlets/DocumentServlet?id=21790
Philipp, Friedrich; Trunk, Carsten
The numerical range of non-negative operators in Krein spaces. - In: Linear algebra and its applications : LAA. - New York, NY : American Elsevier Publ, Bd. 438 (2013), 5, S. 2542-2556

We define and characterize the Krein space numerical range $W(A)$ and the Krein space co-numerical range $W_{\rm co}(A)$ of a non-negative operator $A$ in a Krein space. It is shown that the non-zero spectrum of $A$ is contained in the closure of $W(A)\cap W_{\rm co}(A)$.


http://dx.doi.org/10.1016/j.laa.2012.10.048
Behrndt, Jussi; Luger, Annemarie; Trunk, Carsten
On the negative squares of a class of self-adjoint extensions in Krein spaces. - In: Mathematische Nachrichten. - [S.l.] : Wiley-VCH, ISSN 15222616, Bd. 286 (2013), 2/3, S. 118-148

A description of all exit space extensions with finitely many negative squares of a symmetric operator of defect one is given via Krein's formula. As one of the main results an exact characterization of the number of negative squares in terms of a fixed canonical extension and the behaviour of a function $\tau$ (that determines the exit space extension in Krein's formula) at zero and at infinity is obtained. To this end the class of matrix valued $\mathcal D_\kappa^{n\times n}$-functions is introduced and, in particular, the properties of the inverse of a certain $\mathcal D_\kappa^{2\times 2}$-function which is closely connected with the spectral properties of the exit space extensions with finitely many negative squares is investigated in detail. Among the main tools here are the analytic characterization of the degree of non-positivity of generalized poles of matrix valued generalized Nevanlinna functions and some extensions of recent factorization results.


http://dx.doi.org/10.1002/mana.201000154
Philipp, Friedrich; Strauss, Vladimir; Trunk, Carsten
Local spectral theory for normal operators in Krein spaces. - In: Mathematische Nachrichten. - [S.l.] : Wiley-VCH, ISSN 15222616, Bd. 286 (2013), 1, S. 42-58

Sign type spectra are an important tool in the investigation of spectral properties of selfadjoint operators in Krein spaces. It is our aim to show that also sign type spectra for normal operators in Krein spaces provide insight in the spectral nature of the operator: If the real part and the imaginary part of a normal operator in a Krein space have real spectra only and if the growth of the resolvent of the imaginary part (close to the real axis) is of finite order, then the normal operator possesses a local spectral function defined for Borel subsets of the spectrum which belong to positive (negative) type spectrum. Moreover, the restriction of the normal operator to the spectral subspace corresponding to such a Borel subset is a normal operator in some Hilbert space. In particular, if the spectrum consists entirely out of positive and negative type spectrum, then the operator is similar to a normal operator in some Hilbert space. We use this result to show the existence of operator roots of a class of quadratic operator polynomials with normal coefficients.


http://dx.doi.org/10.1002/mana.201000141
Ilchmann, Achim; Wirth, Fabian
On minimum phase. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 10 S., 270 KB). - (Preprint. - M13,02)

Wir diskutieren Minimalphasigkeit von schwach-stabilen Transferfunktionen; letzteres sind rationale Funktionen, bei denen das Nennerpolynom Nullstellen in der abgeschlossenen linken komplexen Halbebene hat. Minimalphasigkeit wird hier mittels der Ableitung der Argumentfunktion der Transferfunktion definiert. Es wird dann mit Hilfe der Hurwitz-Reflektion gezeigt, daß jede schwach-stabile Transferfunktion eindeutig in ein Produkt von Allpass und minimalphasiger Funktion zerlegt werden kann. Das wesentliche Resultat ist, daß eine schwach-stabile Transferfunktion minimalphasig ist genau dann, wenn das Zählerpolynom der Transferfunktion schwach-stabil ist. Ein weiteres Resultat ist, daß die Nulldynamik einer minimalen Realisation asymptotisch stabil ist genau dann, wenn das Zählerpolynom der Transferfunktion Hurwitz ist. Insbesondere folgt aus asymptotisch stabiler Nulldynamik die Minimalphasigkeit, aber keineswegs umgekehrt. Abschließend zeigen wir, daß ein minimalphasiges System als kanonischer Repräsentant innerhalb der Äquivalenzklasse aller Systeme mit identischem Betragsverhalten interpretiert werden kann.


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Ilchmann, Achim; Reis, Timo
. - Surveys in differential-algebraic equations ; 1. - Berlin [u.a.] : Springer. - VII, 231 S.. - (Differential-algebraic equations forum, DAE-F)
ISBN 3642349277 = 978-3-642-34927-0
Literaturangaben
http://www.gbv.de/dms/ilmenau/toc/728537176.PDF
Berger, Thomas
Bohl exponent for time-varying linear differential-algebraic equations. - In: International journal of control. - London : Taylor & Francis, ISSN 13665820, Bd. 85 (2012), 10, S. 1433-1451
http://dx.doi.org/10.1080/00207179.2012.688872
Berger, Thomas; Ilchmann, Achim; Reis, Timo
Zero dynamics and funnel control of linear differential-algebraic systems. - In: Mathematics of control, signals, and systems : MCSS. - London : Springer, ISSN 1435568X, Bd. 24 (2012), 3, S. 219-263
http://dx.doi.org/10.1007/s00498-012-0085-z
Berger, Thomas; Trenn, Stephan
The quasi-Kronecker form for matrix pencils. - In: SIAM journal on matrix analysis and applications. - Philadelphia, Pa : Soc, ISSN 10957162, Bd. 33 (2012), 2, S. 336-368
http://dx.doi.org/10.1137/110826278
Strauss, Vladimir Abramovich; Trunk, Carsten
Some Sobelev spaces as Pontryagin spaces. - In: Vestnik Južno-Ural&softcy;skogo Gosudarstvennogo Universiteta / Serija matematika, mechanika, fizika. - Čeljabinsk, ISSN 2075809X, Bd. 6Bd. 6.2012, 11 (270), S. 14-23

We show that well known Sobolev spaces can quite naturally be treated as Pontryagin spaces. This point of view gives a possibility to obtain new properties for some traditional objects such as simplest differential operators.


Anderson, Brian D. O.; Ilchmann, Achim; Wirth, Fabian R.
Stabilization of linear time-varying systems. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 21 S., 272,6 KB). - (Preprint. - M12,14)
http://www.db-thueringen.de/servlets/DocumentServlet?id=21511
Möws, Roland
On similarity of indefinite Sturm-Liouville operators. - In: Proceedings in applied mathematics and mechanics : PAMM. - Weinheim [u.a.] : Wiley-VCH, ISSN 16177061, Bd. 12 (2012), 1, S. 771-772
http://dx.doi.org/10.1002/pamm.201210374
Berger, Thomas
On perturbations in the leading coefficient matrix of time-varying index-1 DAEs. - In: Proceedings in applied mathematics and mechanics : PAMM. - Weinheim [u.a.] : Wiley-VCH, ISSN 16177061, Bd. 12 (2012), 1, S. 793-796
http://dx.doi.org/10.1002/pamm.201210382
Knobloch, Jürgen; Vielitz, Martin; Wagenknecht, Thomas
Non-reversible perturbations of homoclinic snaking scenarios. - In: Nonlinearity : ... a journal of the Institute of Physics and the London Mathematical Society. - Bristol : IOP Publ, ISSN 13616544, Bd. 25 (2012), 12, S. 3469-3485
http://dx.doi.org/10.1088/0951-7715/25/12/3469
Winkler, Henrik; Woracek, Harald
Reparametrizations of non trace-normed Hamiltonians. - In: Spectral theory, mathematical system theory, evolution equations, differential and difference equations / International Workshop on Operator Theory and Applications ; 21 (Berlin) : 2010.07.12-16. : 21st International Workshop on Operator Theory and Applications, Berlin, July 2010. - Basel [u.a.] : Birkhäuser, ISBN 978-3-0348-0296-3, (2012), S. 667-690

Behrndt, Jussi; Möws, Roland; Trunk, Carsten
On finite rank perturbations of selfadjoint operators in Krein spaces and eigenvalues in spectral gaps. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 10 S., 150,6 KB). - (Preprint. - M12,12)

It is shown that the finiteness of eigenvalues in a spectral gap of a definitizable or locally definitizable selfadjoint operator in a Krein space is preserved under finite rank perturbations. This results is applied to a class of singular Sturm-Liouville operators with an indefinite weight function.


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Philipp, Friedrich; Trunk, Carsten
The numerical range of non-negative operators in Krein spaces. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 21 S., 177,7 KB). - (Preprint. - M12,11)

We define and characterize the Krein space numerical range W(A) and the Krein space co-numerical range W_{\rm co}(A) of a non-negative operator A in a Krein space. It is shown that the non-zero spectrum of A is contained in the closure of W(A)\cap W_{\rm co}(A).


http://www.db-thueringen.de/servlets/DocumentServlet?id=20973
Berger, Thomas; Ilchmann, Achim; Reis, Timo
Normal forms, high-gain, and funnel control for linear differential-algebraic systems. - In: Control and optimization with differential-algebraic constraints : . - Philadelphia, Pa. : SIAM, Soc. for Industrial and Applied Mathematics, ISBN 978-1-61197-224-5, (2012), S. 127-164

Berger, Thomas
Robustness of stability of time-varying index-1 DAEs. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 44 S., 392,0 KB). - (Preprint. - M12,10)

We study exponential stability and its robustness for time-varying linear index-1 differential-algebraic equations. The effect of perturbations in the leading coefficient matrix is investigated. An appropriate class of allowable perturbations is introduced. Robustness of exponential stability with respect to a certain class of perturbations is proved in terms of the Bohl exponent and perturbation operator. Finally, a stability radius involving these perturbations is introduced and investigated. In particular, a lower bound for the stability radius is derived. The results are presented by means of illustrative examples.


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Berger, Thomas; Trenn, Stephan
Addition to: the quasi-Kronecker form for matrix pencils. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 7 S., 140,1 KB). - (Preprint. - M12,8)
http://www.db-thueringen.de/servlets/DocumentServlet?id=20641
Behrndt, Jussi; Philipp, Friedrich; Trunk, Carsten
Bounds on the non-real spectrum of differential operators with indefinite weights. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 27 S., 276,8 KB). - (Preprint. - M12,07)

Ordinary and partial differential operators with an indefinite weight function can be viewed as bounded perturbations of non-negative operators in Krein spaces. Under the assumption that 0 and infinity are not singular critical points of the unperturbed operator it is shown that a bounded additive perturbation leads to an operator whose non-real spectrum is contained in a compact set and with definite type real spectrum outside this set. The main results are quantitative estimates for this set, which are applied to Sturm-Liouville and second order elliptic partial differential operators with indefinite weights on unbounded domains.


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Ilchmann, Achim
Decentralized tracking of interconnected systems. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 18 S., 231,3 KB). - (Preprint. - M12,06)

Decentralized funnel controllers are applied to finitely many interacting single-input single-output, minimum phase, relative degree one systems in order to track reference signals of each system within a prespecified performance funnel. The reference signals as well as the systems belong to a fairly large class. The result is a generalization of the work by [2].


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Berger, Thomas; Halikias, George; Karcanias, Nicos
Effects of dynamic and non-dynamic element changes in RLC networks. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 27 S., 328 KB). - (Preprint. - M12,04)

The paper deals with the redesign of passive electric networks by changes of single dynamic and non-dynamic elements which may retain, or affect the natural topology of the network. It also deals with the effect of such changes on the natural dynamics of the network, the natural frequencies. The impedance and admittance modeling for passive electrical networks is used which provides a structured, symmetric, integral-differential description, which in the special cases of RC and RL networks is reduced to matrix pencil descriptions. The transformations on the network are expressed as those preserving, or modifying the two natural topologies of the network, the impedance graph and the admittance graph topologies. For the special cases of RC and RL networks we consider the problem of the effect of changes of a single dynamic, or non-dynamic element on the natural frequencies. Using the Determinantal Assignment Framework, it is shown that the family of single parameter variation problems is reduced to equivalent Root Locus problems with the possibility of fixed modes. An explicit characterization of the fixed modes is given and a number of interesting properties of the spectrum are derived such as the interlacing property of poles and zeros for the entire family of Root Locus problems.


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Berger, Thomas; Ilchmann, Achim; Trenn, Stephan
The quasi-Weierstraß form for regular matrix pencils. - In: Linear algebra and its applications : LAA. - New York, NY : American Elsevier Publ, Bd. 436 (2012), 10, S. 4052-4069
http://dx.doi.org/10.1016/j.laa.2009.12.036
Ilchmann, Achim; Pham Huu Anh, Ngoc
Stability and robust stability of positive Volterra systems. - In: International journal of robust and nonlinear control : IFAC affiliated journal. - New York, NY [u.a.] : Wiley, ISSN 10991239, Bd. 22 (2012), 6, S. 604-629
http://dx.doi.org/10.1002/rnc.1712
Berger, Thomas; Reis, Timo
Controllability of linear differential-algebraic systems - a survey. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 48 S., 501 KB). - (Preprint. - M12,03)

Different concepts related to controllability of differential-algebraic equations are described. The class of systems considered consists of linear differential-algebraic equations with constant coefficients. Regularity, which is, loosely speaking, a concept related to existence and uniqueness of solutions for any inhomogeneity, is not required in this article. The concepts of impulse controllability, controllability at infinity, behavioral controllability, strong and complete controllability are described and defined in time-domain. Equivalent criteria that generalize the Hautus test are presented and proved. - Special emphasis is placed on normal forms under state space transformation and, further, under state space, input and feedback transformations. Special forms generalizing the Kalman decomposition and Brunovsky form are presented. Consequences for state feedback design and geometric interpretation of the space of reachable states in terms of invariant subspaces are proved.


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Azizov, Tomas Ya.; Trunk, Carsten
PT symmetric, Hermitian and P-self-adjoint operators related to potentials in PT quantum mechanics. - In: Journal of mathematical physics. - College Park, Md : American Inst. of Physics, ISSN 10897658, Bd. 53 (2012), 1, S. 012109, insges. 18 S.
http://dx.doi.org/10.1063/1.3677368
Arendt, Wolfgang; Ball, Joseph A.; Behrndt, Jussi; Förster, Karl-Heinz; Mehrmann, Volker; Trunk, Carsten
Spectral theory, mathematical system theory, evolution equations, differential and difference equations : 21st International Workshop on Operator Theory and Applications, Berlin, July 2010. - Basel [u.a.] : Birkhäuser. - VIII, 690 S.. - (Operator theory. - 221)
ISBN 303480296X = 978-3-0348-0296-3
Literaturangaben
http://www.gbv.de/dms/ilmenau/toc/671472135.PDF
Homburg, Ale Jan; Jukes, Alice C.; Knobloch, Jürgen; Lamb, Jeroen S. W.
Bifurcation from codimension one relative homoclinic cycles. - In: Transactions of the American Mathematical Society. - Providence, RI : Soc, ISSN 10886850, Bd. 363 (2011), 11, S. 5663-5701
http://dx.doi.org/10.1090/S0002-9947-2011-05193-7
Ilchmann, Achim; Ke, Zhenqing; Logemann, Hartmut
Indirect sampled-data control with sampling period adaptation. - In: International journal of control. - London : Taylor & Francis, ISSN 13665820, Bd. 84 (2011), 2, S. 424-431
http://dx.doi.org/10.1080/00207179.2011.557782
Knobloch, Jürgen; Lloyd, David J. B.; Sandstede, Björn; Wagenknecht, Thomas
Isolas of 2-pulse solutions in homoclinic snaking scenarios. - In: Journal of dynamics and differential equations. - New York, NY [u.a.] : Springer Science + Business Media B.V, ISSN 15729222, Bd. 23 (2011), 1, S. 93-114
http://dx.doi.org/10.1007/s10884-010-9195-9
Hill, Adrian T.; Ilchmann, Achim
Exponential stability of time-varying linear systems. - In: IMA journal of numerical analysis : IMAJNA. - Oxford : Oxford Univ. Press, ISSN 14643642, Bd. 31 (2011), 3, S. 865-885
http://www.dx.doi.org/10.1093/imanum/drq002
Philipp, Friedrich; Ran, André C. M.; Wojtylak, Micha&lstrok;
Local definitizability of T [*]T and TT[*]. - In: Integral equations and operator theory : IEOT. - Berlin : Springer, ISSN 14208989, Bd. 71 (2011), 4, S. 491-508
http://dx.doi.org/10.1007/s00020-011-1913-0
Behrndt, Jussi; Möws, Roland; Trunk, Carsten
Eigenvalue estimates for singular left-definite Sturm-Liouville operators. - In: Journal of spectral theory. - Zürich : EMS Publishing House, ISSN 16640403, Bd. 1 (2011), 3, S. 327-347

The spectral properties of a singular left-definite Sturm-Liouville operator $JA$ are investigated and described via the properties of the corresponding right-definite selfadjoint counterpart $A$ which is obtained by substituting the indefinite weight function by its absolute value. The spectrum of the $J$-selfadjoint operator $JA$ is real and it follows that an interval $(a,b)\subset\dR^+$ is a gap in the essential spectrum of $A$ if and only if both intervals $(-b,-a)$ and $(a,b)$ are gaps in the essential spectrum of the $J$-selfadjoint operator $JA$. As one of the main results it is shown that the number of eigenvalues of $JA$ in $(-b,-a) \cup (a,b)$ differs at most by three of the number of eigenvalues of $A$ in the gap $(a,b)$; as a byproduct results on the accumulation of eigenvalues of singular left-definite Sturm-Liouville operators are obtained. Furthermore, left-definite problems with symmetric and periodic coefficients are treated, and several examples are included to illustrate the general results.


http://dx.doi.org/10.4171/JST/14
Philipp, Friedrich; Szafraniec, Franciszek Hugon; Trunk, Carsten
Selfadjoint operators in S-spaces. - In: Journal of functional analysis. - Amsterdam [u.a.] : Elsevier, ISSN 10960783, Bd. 260 (2011), 4, S. 1045-1059

We study S-spaces and operators therein. An S-space is a Hilbert space with an additional inner product given by $\Skindef := (U\,\cdot\,,-)$, where $U$ is a unitary operator. We investigate spectral properties of selfadjoint operators in S-spaces. We show that their spectrum is symmetric with respect to the real axis. As a main result we prove that for each selfadjoint operator $A$ in an S-space we find an inner product which turns $\bez$ into a Krein space and $A$ into a selfadjoint operator therein. As a consequence we get a new simple condition for the existence of invariant subspaces of selfadjoint operators in Krein spaces, which provides a different insight into this well know and in general unsolved problem.


http://dx.doi.org/10.1016/j.jfa.2010.10.023
Azizov, Tomas Ya.; Behrndt, Jussi; Jonas, Peter; Trunk, Carsten
Spectral points of definite type and type π for linear operators and relations in Krein spaces. - In: Journal of the London Mathematical Society. - Oxford : Wiley, ISSN 14697750, Bd. 83 (2011), 3, S. 768-788

Spectral points of positive and negative type, and type $\pi_{+}$ and type $\pi_{-}$ for closed linear operators and relations in Krein spaces are introduced with the help of approximative eigensequences. The main objective of the paper is to study these sign type properties in the non-selfadjoint case under various kinds of perturbations, e.g. compact perturbations and perturbations small in the gap metric. Many of the obtained perturbation results are also new for the special case of bounded and unbounded selfadjoint operators in Krein spaces.


http://dx.doi.org/10.1112/jlms/jdq098
Behrndt, Jussi; Hassi, Seppo; Snoo, Henk; Wietsma, Rudi; Winkler, Henrik
Linear fractional transformations of Stieltjes functions. - In: Proceedings in applied mathematics and mechanics : PAMM. - Weinheim [u.a.] : Wiley-VCH, ISSN 16177061, Bd. 11 (2011), 1, S. 887-888
http://dx.doi.org/10.1002/pamm.201110430
Hennig, Eckhard; Krauße, Dominik; Schäfer, Eric; Sommer, Ralf; Trunk, Carsten; Winkler, Henrik
Frequency compensation for a class of DAE's arising in electrical circuits. - In: Proceedings in applied mathematics and mechanics : PAMM. - Weinheim [u.a.] : Wiley-VCH, ISSN 16177061, Bd. 11 (2011), 1, S. 837-838

Structured perturbations of regular pencils of the form $sE-A$, $E,A\in\dR^{n\times n}, ˜s\in\dC,$ are considered which model the addition of a capacitance $c$ in an electrical circuit in order to improve the frequency response.


http://dx.doi.org/10.1002/pamm.201110407
Winkler, Henrik; Behrndt, Jussi; Hassi, Seppo; Snoo, Henk; Wietsma, Rudi
Linear fractional transformations of Nevanlinna functions associated with a nonnegative operator. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 26 S., 436,5 KB). - (Preprint. - M11,18)
http://www.db-thueringen.de/servlets/DocumentServlet?id=19505
Winkler, Henrik; Woracek, Harald
Reparametrizations of non trace-normed Hamiltonians. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 23 S., 344,7 KB). - (Preprint. - M11,17)

We consider a Hamiltonian system of the form y0(x) = JH(x)y(x), with a locally integrable and nonnegative 2_2-matrix valued Hamiltonian H(x). In the literature dealing with the operator theory of such equations, it is often required in addition that the Hamiltonian H is trace{normed, i.e. satis_es trH(x) _ 1. However, in many examples this property does not hold. The general idea is that one can reduce to the trace{normed case by applying a suitable change of scale (reparametrization). In this paper we justify this idea and work out the notion of reparametrization in detail.


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Knobloch, Jürgen; Rieß, Thorsten; Vielitz, Martin
Nonreversible homoclinic snaking. - In: Dynamical systems : an international journal. - London : Taylor & Francis, ISSN 14689375, Bd. 26 (2011), 3, S. 335-365
http://dx.doi.org/10.1080/14689367.2011.592488
Kuzhel, Sergii; Trunk, Carsten
On a class of J-self-adjoint operators with empty resolvent set. - In: Journal of mathematical analysis and applications. - Amsterdam [u.a.] : Elsevier, Bd. 379 (2011), 1, S. 272-289
http://dx.doi.org/10.1016/j.jmaa.2010.12.048
Snoo, Henk; Winkler, Henrik; Wojtylak, Michal
Zeros of nonpositive type of generalized Nevanlinna functions with one negative square. - In: Journal of mathematical analysis and applications. - Amsterdam [u.a.] : Elsevier, Bd. 382 (2011), 1, S. 399-417
http://dx.doi.org/10.1016/j.jmaa.2011.04.060
Azizov, Tomas Ya.; Trunk, Carsten
PT symmetric, hermitian and P-self-adjoint operators related to potentials in PT quantum mechanics. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 28 S., 189,9 KB). - (Preprint. - M11,15)

In the recent years a generalization H=p^2 + x^2(ix)^\epsilon of the harmonic oscillator using a complex deformation was investigated, where \epsilon is a real parameter. Here, we will consider the most simple case: \epsilon even and x real. We will give a complete characterization of three different classes of operators associated with the differential expression H: The class of all self-adjoint (Hermitian) operators, the class of all PT symmetric operators and the class of all P-self-adjoint operators. Surprisingly, some of the PT symmetric operators associated to this expression have no resolvent set.


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Berger, Thomas; Ilchmann, Achim; Reis, Timo
Normal forms, high-gain and funnel control for linear differential-algebraic systems. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 35 S., 563,1 KB). - (Preprint. - M11,14)

We consider linear differential-algebraic m-input m-output systems with positive strict relative degree or proper inverse transfer function; in the single-input single-output case these two disjoint classes make the whole of all linear DAEs without feedthrough term. Structural properties - such as normal forms (i.e. the counterpart to the Byrnes-Isidori form for ODE systems), zero dynamics, and high-gain stabilizability - are analyzed for two purposes: first, to gain insight into the system classes and secondly, to solve the output regulation problem by funnel control. The funnel controller achieves tracking of a class of reference signals within a pre-specified funnel; this means in particular, the transient behaviour of the output error can be specified and the funnel controller does neither incorporate any internal model for the reference signals nor any identification mechanism, it is simple in its design. The results are illuminated by position and velocity control of a mechanical system encompassing springs, masses, and dampers.


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Hennig, Eckhard; Krauße, Dominik; Schäfer, Eric; Sommer, Ralf; Trunk, Carsten; Winkler, Henrik
Frequency compensation for a class of DAE's arising in electrical circuits. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 5 S., 115,2 KB). - (Preprint. - M11,11)
http://www.db-thueringen.de/servlets/DocumentServlet?id=18489
Berger, Thomas
Bohl exponents for time-varying linear differential-algebraic equations. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 25 S., 429,5 KB). - (Preprint. - M11,09)

We study stability of linear time-varying differential-algebraic equations (DAEs). The Bohl exponent is introduced and finiteness of the Bohl exponent is characterized, the equivalence of exponential stability and a negative Bohl exponent is shown and shift properties are derived. We also show that the Bohl exponent is invariant under the set of Bohl transformations. For the class of DAEs which possess a transition matrix introduced in this paper, the Bohl exponent is exploited to characterize boundedness of solutions of a Cauchy problem and robustness of exponential stability.


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Behrndt, Jussi; Philipp, Friedrich; Trunk, Carsten
A perturbation approach to differential operators with indefinite weights. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 18 S., 210,5 KB). - (Preprint. - M11,08)
http://www.db-thueringen.de/servlets/DocumentServlet?id=18137
Berger, Thomas; Trenn, Stephan
The quasi-Kronecker form for matrix pencils. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 22 S., 535 KB). - (Preprint. - M11,07)

We study singular matrix pencils and show that the so called Wong sequences yield a quasi-Kronecker form. This form decouples the matrix pencil into an underdetermined part, a regular part and an overdetermined part. This decoupling is sufficient to fully characterize the solution behaviour of the differential-algebraic equations associated with the matrix pencil. Furthermore, the Kronecker canonical form is a simple corollary of our result, hence, in passing by, we also provide a new proof for the Kronecker canonical form. The results are illustrated with an example given by a simple electrical circuit.


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Labrousse, Jean-Philippe; Sandovici, Arian; Snoo, Henk; Winkler, Henrik
Closed linear relations and their regular points. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 24 S., 290 KB). - (Preprint. - M11,03)
http://www.db-thueringen.de/servlets/DocumentServlet?id=17546
Snoo, Henk; Winkler, Henrik; Wojtylak, Michal
Zeros of nonpositive type of generalized Nevanlinna functions with one negative square. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 31 S., 318,6 KB). - (Preprint. - M11,02)
http://www.db-thueringen.de/servlets/DocumentServlet?id=17544
Behrndt, Jussi; Möws, Roland; Trunk, Carsten
Eigenvalue estimates for singular left-definite Sturm-Liouville operators. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 15 S., 379,8 KB). - (Preprint. - M11,01)

The spectral properties of a singular left-definite Sturm-Liouville operator JA are investigated and described via the properties of the corresponding right-definite selfadjoint counterpart A which is obtained by substituting the indefinite weight function by its absolute value. The spectrum of the J-selfadjoint operator JA is real and it follows that an interval (a; b) \subset {\Bbb R}+ is a gap in the essential spectrum of A if and only if both intervals (-b;-a) and (a; b) are gaps in the essential spectrum of the J-selfadjoint operator JA. As one of the main results it is shown that the number of eigenvalues of JA in (-b;-a) [ (a; b) di ers at most by three of the number of eigenvalues of A in the gap (a; b); as a byproduct results on the accumulation of eigenvalues of singular left-definite Sturm-Liouville operators are obtained. Furthermore, left-definite problems with symmetric and periodic coefficients are treated, and several examples are included to illustrate the general results


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Ilchmann, Achim; Logemann, Hartmut; Ryan, Eugene P.
Tracking with prescribed transient performance for hysteretic systems. - In: SIAM journal on control and optimization. - Philadelphia, Pa : Soc, ISSN 10957138, Bd. 48 (2010), 7, S. 4731-4752
http://dx.doi.org/10.1137/070691863
Ilchmann, Achim; Mueller, Markus
Robustness of funnel control in the gap metric. - In: 2010 49th IEEE Conference on Decision and Control : (CDC) ; 15 - 17 Dec. 2010. - Piscataway, NJ : IEEE / IEEE Conference on Decision and Control ; 49 (Atlanta, Ga.) : 2010.12.15-17., ISBN 978-1-4244-7746-3, (2010), S. 609-614

http://dx.doi.org/10.1109/CDC.2010.5718083
Ilchmann, Achim; Mueller, Markus
Robustness of funnel control in the gap metric. - In: SIAM journal on control and optimization. - Philadelphia, Pa : Soc, ISSN 10957138, Bd. 48 (2010), 5, S. 3169-3190
http://dx.doi.org/10.1137/090758891
Homburg, Ale Jan; Knobloch, Jürgen
Switching homoclinic networks. - In: Dynamical systems : an international journal. - London : Taylor & Francis, ISSN 14689375, Bd. 25 (2010), 3, S. 351-358
Corrigendum. - Bd. 25.2010, 3, S. 443
http://dx.doi.org/10.1080/14689361003769770
Azizov, Tomas Ya.; Jonas, Peter; Trunk, Carsten
Small perturbations of selfadjoint and unitary operators in Krein spaces. - In: Journal of operator theoryJournal of operator theory. - Bucharest : The Theta Foundation : . - Bucharest : The Theta Foundation, ISSN 03794024, Bd. 64 (2010), 2, S. 401-416

We investigate the behaviour of the spectrum of selfadjoint operators in Krein spaces under perturbations with uniformly dissipative operators. Moreover we consider the closely related problem of the perturbation of unitary operators with uniformly bi-expansive. The obtained perturbation results give a new characterization of spectral points of positive type and of type $\pi_{+}$ of selfadjoint (resp.\ unitary) operators in Krein spaces.


Hopfe, Norman; Ilchmann, Achim; Ryan, Eugene P.
Funnel control with saturation: nonlinear SISO systems. - In: IEEE transactions on automatic control. - New York, NY : Institute of Electrical and Electronics Engineers, ISSN 15582523, Bd. 55 (2010), 9, S. 2177-2182
http://dx.doi.org/10.1109/TAC.2010.2051735
Henn, Mark-Alexander; Mehl, Christian; Trunk, Carsten
Hyponormal and strongly hyponormal matrices in inner product spaces. - In: Linear algebra and its applications : LAA. - New York, NY : American Elsevier Publ, Bd. 433 (2010), 6, S. 1055-1076
http://dx.doi.org/10.1016/j.laa.2010.04.050
Behrndt, Jussi; Luger, Annemarie; Trunk, Carsten
On the negative squares of a class of self-adjoint extensions in Krein spaces. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 34 S., 386 KB). - (Preprint. - M10,16)

A description of all exit space extensions with finitely many negative squares of a symmetric operator of defect one is given via Krein's formula. As one of the main results an exact characterization of the number of negative squares in terms of a fixed canonical extension and the behaviour of a function t (that determines the exit space extension in Krein's formula) at zero and at infinity is obtained. To this end the class of matrix valued D k n×n -functions is introduced and, in particular, the properties of the inverse of a certain D k 2×2 -function which is closely connected with the spectral properties of the exit space extensions with finitely many negative squares is investigated in detail. Among the main tools here are the analytic characterization of the degree of non-positivity of generalized poles of matrix valued generalized Nevanlinna functions and some extensions of recent factorization results.


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Berger, Thomas; Ilchmann, Achim; Reis, Timo
Zero dynamics and funnel control of linear differential-algebraic systems. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 35 S., 674 KB). - (Preprint. - M10,15)

We study the class of linear differential-algebraic m-input m-output systems which have a transfer function with proper inverse. A sufficient condition for the transfer function to have proper inverse it that the system has 'strict and non-positive relative degree'. We present two main results: First, a so called 'zero dynamics form' is derived: this form is - within the class of system equivalence - a simple ("almost normal") form of the DAE; it is a counterpart to the well-known Byrnes-Isidori form for ODE systems with strictly proper transfer function. The 'zero dynamics form' is exploited to characterize structural properties such as asymptotically stable zero dynamics, minimum phase, and high-gain stabilizability. The zero dynamics are characterized by (A,E,B)-invariant subspaces. Secondly, it is shown that the 'funnel controller' (that is a static nonlinear output error feedback) achieves, for all DAE systems with asymptotically stable zero dynamics and transfer function with proper inverse, tracking of a reference signal by the output signal within a pre-specified funnel. This funnel determines the transient behaviour.


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Kuzhel, Sergii; Trunk, Carsten
On a class of J-self-adjoint operators with empty resolvent set. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 29 S., 257,3 KB). - (Preprint. - M10,11)
http://www.db-thueringen.de/servlets/DocumentServlet?id=16642
Philipp, Friedrich; Strauss, Vladimir A.; Trunk, Carsten
Local spectral theory for normal operators in Krein spaces. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 18 S., 172 KB). - (Preprint. - M10,09)

Sign type spectra are an important tool in the investigation of spectral properties of selfadjoint operators in Krein spaces. It is our aim to show that also sign type spectra for normal operators in Krein spaces provide insight in the spectral nature of the operator: If the real part and the imaginary part of a normal operator in a Krein space have real spectra only and if the growth of the resolvent of the imaginary part (close to the real axis) is of nite order, then the normal operator possesses a local spectral function dened for Borel subsets of the spectrum which belong to positive (negative) type spectrum. Moreover, the restriction of the normal operator to the spectral subspace corresponding to such a Borel subset is a normal operator in some Hilbert space. In particular, if the spectrum consists entirely out of positive and negative type spectrum, then the operator is similar to a normal operator in some Hilbert space.


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Berger, Thomas; Ilchmann, Achim
On stability of time-varying linear differential-algebraic equations. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 25 S., 284,9 KB). - (Preprint. - M10,12)

We develop a stability theory for time-varying linear differential algebraic equations (DAEs). Standard stability concepts for ODEs are formulated for DAEs and characterized. Lyapunovs direct method is derived as well as the converse of the stability theorems. Stronger results are achieved for DAEs which are transferable into standard canonical form; in this case the existence of the generalized transition matrix is exploited.


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Trunk, Carsten
Spectral theory for second order systems and indefinite Sturm-Liouville problems. - getr. Zählung
Ilmenau : Techn. Univ., Habil.-Schr., 2010
http://www.gbv.de/dms/ilmenau/toc/634464116.PDF
Berger, Thomas; Ilchmann, Achim
Time-varying linear DAEs transferable into standard canonical form. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 19 S., 270,1 KB). - (Preprint. - M10,07)
http://www.db-thueringen.de/servlets/DocumentServlet?id=16192
Hackl, Christoph; Hopfe, Norman; Ilchmann, Achim; Müller, Markus; Trenn, Stephan
Funnel control for systems with relative degree two. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 36 S., 523,7 KB). - (Preprint. - M10,06)

Tracking of reference signals yref(&hahog;) by the output y(&hahog;) of linear (as well as a considerably large class of nonlinear) single-input, single-output system is considered. The system is assumed to have strict relative degree two with ("weak") stable zero dynamics. The control objective is tracking of the error e = y - yref and its derivative e&hahog; within two prespecified performance funnels, resp. This is achieved by the so called 'funnel controller': u(t) = -k0(t)2e(t) - k1(t)e&hahog;(t), where the simple proportional error feedback has gain functions k0 and k1 designed in such a way to preclude contactof e and e&hahog; with the funnel boundaries, resp. The funnel controller also ensures boundedness of all signals. --- We also show that the same funnel controller is (i) applicable to relative degree one systems, (ii) allows for input constraints provided a feasibility condition (formulated in terms of the system data, the saturation bounds, the funnel data, bounds on the reference signal and the initial state) holds, (iii) is robust in terms of the gap metric: if a system is sufficiently close to a system with relative degree two, stable zero dynamics and positive high-frequency gain, but does not necessarily have these properties, then for small initial values the funnel controller also achieves the control objective. Finally, we illustrate the theoretical results by experimental results: the funnel controller is applied to a rotatory mechanical system for position control.


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Berger, Thomas; Ilchmann, Achim
Zero dynamics of time-varying linear systems. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 23 S., 297,2 KB). - (Preprint. - M10,05)

The Byrnes-Isidori form with respect to the relative degree is studied for time-varying linear multi-input, multi-output systems. It is clarified in which sense this form is a normal form. (A,B)-invarianttime-varying subspaces are defined and the maximal(A,B)-invariant time-varying subspace included in the kernel of C is characterized. This is exploited to characterize the zero dynamics of the system. Finally, a high-gain derivative output feedback controller is introduced for the class of systems with higher relative degree and stable zero dynamics. All results are also new for time-invariant linear systems.


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Azizov, Tomas Ya.; Trunk, Carsten
On domains of PT symmetric operators related to -y"(x) + (-1) n x 2n y(x). - In: Journal of physics / A. - Bristol : IOP Publ, ISSN 17518121, Bd. 43Bd. 43.2010, 17, 175303, insges. 13 S.
http://dx.doi.org/10.1088/1751-8113/43/17/175303
Behrndt, Jussi; Philipp, Friedrich
Spectral analysis of singular ordinary differential operators with indefinite weights. - In: Journal of differential equations. - Orlando, Fla : Elsevier, ISSN 10902732, Bd. 248 (2010), 8, S. 2015-2037
http://dx.doi.org/10.1016/j.jde.2009.11.026
Hopfe, Norman; Ilchmann, Achim; Ryan, Eugene P.
Funnel control with saturation: linear MIMO systems. - In: IEEE transactions on automatic control. - New York, NY : Institute of Electrical and Electronics Engineers, ISSN 15582523, Bd. 55 (2010), 2, S. 532-538
http://dx.doi.org/10.1109/TAC.2009.2037475
Trunk, Carsten
Analyticity of semigroups related to a class of block operator matrices. - In: / International Workshop on Operator Theory and Applications ; 18 (Potchefstroom) : 2007.07.03-06. : ., ISBN 978-3-0346-0173-3, (2010), S. 257-271

Knobloch, Jürgen; Rieß, Thorsten
Lin's method for heteroclinic chains involving periodic orbits. - In: Nonlinearity : ... a journal of the Institute of Physics and the London Mathematical Society. - Bristol : IOP Publ, ISSN 13616544, Bd. 23 (2010), 1, S. 23-54
http://dx.doi.org/10.1088/0951-7715/23/1/002
Behrndt, Jussi; Förster, Karl-Heinz; Trunk, Carsten
Recent advances in operator theory in Hilbert and Krein spaces : [7th Workshop on Operator Theory in Krein Spaces and Spectral Analysis, which was held at the Technische Universität Berlin, Germany, December 13 to 16, 2007]. - Basel [u.a.] : Birkhäuser. - XV, 307 S.. - (Operator theory. - 198)
Literaturangaben
http://www.gbv.de/dms/ilmenau/toc/602554489.PDF
Behrndt, Jussi; Philipp, Friedrich; Trunk, Carsten
Definitizability of a class of J-selfadjoint operators with applications. - In: Proceedings in applied mathematics and mechanics : PAMM. - Weinheim [u.a.] : Wiley-VCH, ISSN 16177061, Bd. 9 (2009), 1, S. 665-666
http://dx.doi.org/10.1002/pamm.200910302
Behrndt, Jussi; Möws, Roland; Trunk, Carsten
Singular indefinite Sturm-Liouville operators with a spectral gap. - In: Proceedings in applied mathematics and mechanics : PAMM. - Weinheim [u.a.] : Wiley-VCH, ISSN 16177061, Bd. 9 (2009), 1, S. 669-670
http://dx.doi.org/10.1002/pamm.200910304
Liberzon, Daniel; Trenn, Stephan
On stability of linear switched differential algebraic equations. - In: Proceedings of the 48th IEEE Conference on Decision and Control, 2009 : held jointly with the 2009 28th Chinese Control Conference ; CDC/CCC 2009 ; 15 - 18 Dec. 2009, Shanghai, China. - Piscataway, NJ : IEEE / IEEE Conference on Decision and Control ; 48 (Shanghai) : 2009.12.15-18., ISBN 978-1-4244-3871-6, (2009), S. 2156-2161

http://dx.doi.org/10.1109/CDC.2009.5400076
Ilchmann, Achim; Mueller, Markus
Robustness of [lambda]-tracking and funnel control in the gap metric. - In: Proceedings of the 48th IEEE Conference on Decision and Control, 2009 : held jointly with the 2009 28th Chinese Control Conference ; CDC/CCC 2009 ; 15 - 18 Dec. 2009, Shanghai, China. - Piscataway, NJ : IEEE / IEEE Conference on Decision and Control ; 48 (Shanghai) : 2009.12.15-18., ISBN 978-1-4244-3871-6, (2009), S. 85-90

http://dx.doi.org/10.1109/CDC.2009.5400170
Behrndt, Jussi; Katatbeh, Qutaibeh; Trunk, Carsten
Non-real eigenvalues of singular indefinite Sturm-Liouville operators. - In: Proceedings of the American Mathematical Society. - Providence, RI : Soc, ISSN 00029939, Bd. 137 (2009), 11, S. 3797-3806
Trenn, Stephan
Regularity of distributional differential algebraic equations. - In: Mathematics of control, signals, and systems : MCSS. - London : Springer, ISSN 1435568X, Bd. 21 (2009), 3, S. 229-264
http://dx.doi.org/10.1007/s00498-009-0045-4
Azizov, Tomas Ya.; Trunk, Carsten
On domains of PT symmetric operators related to -y"(x) + (-1) n x 2n y(x). - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 15 S., 186,1 KB). - (Preprint. - M09,30)
http://www.db-thueringen.de/servlets/DocumentServlet?id=14408
Steigenberger, Joachim; Abeßer, Harald
Quasistatic inflation processes within compliant tubes. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 30 S., 326,7 KB). - (Preprint. - M09,29)
http://www.db-thueringen.de/servlets/DocumentServlet?id=14407
Abeßer, Harald; Steigenberger, Joachim
Ein Optimalsteuerproblem mit einem speziellen Zielfunktional und Zustandsbeschränkungen in einem Teilintervall bei beliebigem Relativgrad. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 21 S., 667,4 KB). - (Preprint. - M09,28)
http://www.db-thueringen.de/servlets/DocumentServlet?id=14422
Hopfe, Norman; Ilchmann, Achim; Ryan, Eugene P.
Funnel control with saturation: nonlinear SISO systems. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 15 S., 226,9 KB). - (Preprint. - M09,27)
http://www.db-thueringen.de/servlets/DocumentServlet?id=14014
Ilchmann, Achim; Ryan, Eugene P.
Performance funnels and tracking control. - In: International journal of control. - London : Taylor & Francis, ISSN 13665820, Bd. 82 (2009), 10, S. 1828-1840
http://dx.doi.org/10.1080/00207170902777392
Jacob, Birgit; Trunk, Carsten
Spectrum and analyticity of semigroups arising in elasticity theory and hydromechanics. - In: Semigroup forum. - New York, NY : Springer, ISSN 14322137, Bd. 79 (2009), 1, S. 79-100
http://dx.doi.org/10.1007/s00233-009-9148-y
Ilchmann, Achim; Pham Huu Anh, Ngoc
On positivity and stability of linear time-varying Volterra equations. - In: Positivity : an international journal devoted to the theory and applications of positivity in analysis. - Dordrecht [u.a.] : Springer Science + Business Media B.V, ISSN 15729281, Bd. 13 (2009), 4, S. 671-681
http://dx.doi.org/10.1007/s11117-008-2235-6
Beck, Margaret; Knobloch, Jürgen; Lloyd, David J. B.; Sandstede, Björn; Wagenknecht, Thomas
Snakes, ladders, and isolas of localized patterns. - In: SIAM journal on mathematical analysis. - Philadelphia, Pa : SIAM, ISSN 10957154, Bd. 41 (2009), 3, S. 936-972
http://dx.doi.org/10.1137/080713306
French, Mark; Ilchmann, Achim; Mueller, Markus
Robust stabilization by linear output delay feedback. - In: SIAM journal on control and optimization. - Philadelphia, Pa : Soc, ISSN 10957138, Bd. 48 (2009), 4, S. 2533-2561
http://dx.doi.org/10.1137/080726070
Mueller, Markus
Output feedback control and robustness in the gap metric. - Ilmenau : Univ.-Verl. Ilmenau. - Online-Ressource (PDF-Datei: 254 S., 1,82 MB)
Ilmenau : Techn. Univ., Diss., 2009

Die vorgelegte Arbeit behandelt den Entwurf und die Robustheit von drei verschiedenen Regelstrategien für lineare Differentialgleichungssysteme mit mehrdimensionalen Ein- und Ausgangssignalen (MIMO): Stabilisierung durch Ausgangs-Ableitungs-Rückführung, Lambda-tracking und Funnel-Regelung. Damit diese Regler bei der Anwendung auf ein lineares System die gewünschten Stabilisierung/Regelung erbringen, ist eine explizite Kenntnis der Systemmatrizen nicht notwendig. Es müssen nur strukturelle Eigenschaften des Systems bekannt sein: der Relativgrad, dass das System minimalphasig ist, und dass die sogenannte "high-frequency gain" Matrix positiv definit ist. Diese stukturellen Eigenschaften werden für MIMO-Systeme in den ersten Kapiteln der Arbeit ausführlich behandelt. Für MIMO-Systeme mit nicht striktem Relativgrad wird eine Normalform hergeleitet, die die gleichen Eigenschaften wie die bekannte Normalform für SISO-Systeme oder MIMO-Systeme mit striktem Relativgrad aufweist. Die Normalform sowie Minimalphasigkeit und Positivität der "high-frequency gain" Matrix bilden die Grundlage dafür, dass die oben genannten Regelstrategien Systeme mit diesen Eigenschaften im jeweiligen Sinn stabilisieren. Robustheit bzw. robuste Stabilisierung beschreibt folgendes Prinzip: falls ein geschlossener Kreis aus einem linearen System und einem Regler in gewissem Sinne stabil ist und die Gap-Metrik (der Abstand) zwischen dem im geschlossenen Kreis betrachteten System und einem anderen "neuen" System hinreichend klein ist, so ist der geschlossene Kreis aus dem "neuen" System und dem gleichen Regler wieder stabil. Die gleiche Aussage stimmt auch für den Fall, dass man den Regler und nicht das System austauscht. Für Ausgangs-Ableitungs-Rückführung wird gezeigt, dass, falls diese ein System stabilisiert, die auftretenden Ableitungen des Ausgangs durch Euler-Approximationen der Ableitungen ersetzt werden können, falls diese hinreichend genau sind. Für Lambda-tracking und Funnel-Regelung wird gezeigt, dass beide Regler auch für die Stabilisierung linearer Systeme verwendet werden können, die einen geringen Abstand zu einem System haben, dass die o.g. Voraussetzungen erfüllt, selbst diese Voraussetzungen aber nicht erfüllen.


http://d-nb.info/997223944/04
Trenn, Stephan
Distributional differential algebraic equations. - Ilmenau : Univ.-Verl. Ilmenau. - Online-Ressource (PDF-Datei: 189 S., 1,15 MB)
Ilmenau : Techn. Univ., Diss., 2009

Lineare implizite Differentialgleichungen der Form Ex'=Ax+f werden untersucht. Da die Matrix E nicht als invertierbar angenommen wird, enthält das Gleichungssystem neben den Differentialgleichungen auch algebraische Gleichungen. Deshalb werden diese Gleichungen differential-algebraische Gleichungen (differential algebraic equations, DAEs) genannt. Ein wesentliches Ziel der Dissertation ist es, Distributionen (oder verallgemeinerte Funktionen) als Lösungen zuzulassen und gleichzeitig soll es möglich sein, zeitvariante DAEs zu untersuchen, deren Koeffizientenmatrizen Sprünge haben können. Dazu wird zunächst ein geeigneter Lösungsraum hergeleitet. Insbesondere ist es mit diesem Lösungsraum möglich, die wichtige Klasse der geschalteten DAEs (switched DAEs) zu untersuchen. Als Lösungsraum wird der Raum der stückweise glatten Distributionen (piecewise-smooth distributions) eingeführt. Für diesen Raum ist es möglich, eine Multiplikation zu definieren, so dass auch DAEs betrachtet werden können, deren Koeffizienten ebenfalls distributionelle Einträge haben. Eine distributionelle DAE ist eine Gleichung der Form Ex'=Ax+f, bei der die Matrizen E und A stückweise glatte Distributionen als Einträge enthalten und die Lösungen x sowie die Inhomogenitäten f ebenfalls stückweise glatte Distributionen sind. Für distributionelle DAEs wird die Existenz und Eindeutigkeit von Lösungen untersucht, dazu wird das Konzept der Regularität für distributionelle DAEs eingeführt. Es werden notwendige und hinreichende Bedingungen für die Existenz und Eindeutigkeit von Lösungen hergeleitet. Als Spezialfälle werden die beiden Gleichungen x'=Ax+f (so genannte distributionelle ODEs) und Nx'=x+f (so genannte reine distributionelle DAEs) untersucht, für die explizite Lösungsformeln angegeben werden können. Geschaltete DAEs sind distributionelle DAEs mit stückweise konstanten Koeffizientenmatrizen. Es werden hinreichende Bedingung hergeleitet, die sicherstellen, dass die Lösungen von geschalteten DAEs keine Impulse enthalten. Weiterhin wird untersucht, unter welchen Bedingungen das beliebige Schalten zwischen stabilen Teilsystemen zu einem stabilen Gesamtsystem führt. Schließlich werden Steuerbarkeit und Beobachtbarkeit für distributionelle DAEs untersucht. Hierbei wird berücksichtigt, dass das Eingangssignal Impulse enthalten kann und damit theoretisch eine "instantane" Steuerung möglich ist. Für eine DAE der Form N'=x+bu, y=cx, mit Konstanten, nilpotenten N sowie konstanten Vektoren b und c wird eine Normalform angegeben, die eine einfache Charakterisierung der Steuerbarkeit und Beobachtbarkeit ermöglicht.


http://zbmath.org/?q=an:1360.34002
Berger, Thomas; Ilchmann, Achim; Trenn, Stephan
The quasi-Weierstraß form for regular matrix pencils. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 18 S., 251 KB). - (Preprint. - M09,21)
http://www.db-thueringen.de/servlets/DocumentServlet?id=13557
Karabash, Illya; Trunk, Carsten
Spectral properties of singular Sturm-Liouville operators with indefinite weight sgn x. - In: Proceedings / A. - Cambridge [u.a.] : Cambridge Univ. Press, ISSN 14737124, Bd. 139 (2009), 3, S. 483-503
http://dx.doi.org/10.1017/S0308210507000686
Pham Huu Anh, Ngoc
On positivity and stability of linear Volterra systems with delay. - In: SIAM journal on control and optimization. - Philadelphia, Pa : Soc, ISSN 10957138, Bd. 48 (2009), 3, S. 1939-1960
http://dx.doi.org/10.1137/080740040
Pham Huu Anh, Ngoc; Murakami, Satoru; Naito, Toshiki; Shin, Jong Son; Nagabuchi, Y.
On positive linear Volterra-Stieltjes differential systems. - In: Integral equations and operator theory : IEOT. - Berlin : Springer, ISSN 14208989, Bd. 64 (2009), 3, S. 325-355
http://dx.doi.org/10.1007/s00020-009-1692-z
Ilchmann, Achim; Mueller, Markus
Robustness of funnel control in the gap metric. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 21 S., 363,1 KB). - (Preprint. - M09,19)
http://www.db-thueringen.de/servlets/DocumentServlet?id=13277
Hill, Adrian T.; Ilchmann, Achim
Exponential stability of time-varying linear systems. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 25 S., 266,8 KB). - (Preprint. - M09,18)
http://www.db-thueringen.de/servlets/DocumentServlet?id=13274
Azizov, Tomas Ya.; Behrndt, Jussi; Jonas, Peter; Trunk, Carsten
Compact and finite rank perturbations of closed linear operators and relations in Hilbert spaces. - In: Integral equations and operator theory : IEOT. - Berlin : Springer, ISSN 14208989, Bd. 63 (2009), 2, S. 151-163
http://dx.doi.org/10.1007/s00020-008-1650-1
Pham Huu Anh, Ngoc; Naito, Toshiki; Shin, Jong Son; Murakami, Satoru
Stability and robust stability of positive linear Volterra difference equations. - In: International journal of robust and nonlinear control : IFAC affiliated journal. - New York, NY [u.a.] : Wiley, ISSN 10991239, Bd. 19 (2009), 5, S. 552-568
http://dx.doi.org/10.1002/rnc.1335
Ilchmann, Achim; Schuster, Hans
PI-funnel control for two mass systems. - In: IEEE transactions on automatic control. - New York, NY : Institute of Electrical and Electronics Engineers, ISSN 15582523, Bd. 54 (2009), 4, S. 918-923
http://dx.doi.org/10.1109/TAC.2009.2013013
Hopfe, Norman; Ilchmann, Achim; Ryan, Eugene P.
Funnel control with saturation: linear MIMO systems. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 15 S., 189,7 KB). - (Preprint. - M09,05)
http://www.db-thueringen.de/servlets/DocumentServlet?id=12958
Liberzon, Daniel; Trenn, Stephan
On stability of linear switched differential algebraic equations. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 7 S., 710,1 KB). - (Preprint. - M09,04)
http://www.db-thueringen.de/servlets/DocumentServlet?id=12565
Trenn, Stephan
Impulse free solutions for switched differential algebraic equations. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 16 S., 220,2 KB). - (Preprint. - M09,03)
http://www.db-thueringen.de/servlets/DocumentServlet?id=12277
Mueller, Markus
Normal form for linear systems with respect to its vector relative degree. - In: Linear algebra and its applications : LAA. - New York, NY : American Elsevier Publ, Bd. 430 (2009), 4, S. 1292-1312
http://dx.doi.org/10.1016/j.laa.2008.10.014
Trenn, Stephan
A normal form for pure differential algebraic systems. - In: Linear algebra and its applications : LAA. - New York, NY : American Elsevier Publ, Bd. 430 (2009), 4, S. 1070-1084
http://dx.doi.org/10.1016/j.laa.2008.10.004
Philipp, Friedrich; Trunk, Carsten
G-self-adjoint operators in Almost Pontryagin spaces. - In: / Workshop on Operator Theory in Krein Spaces and Operator Polynomials ; 6 (Berlin) : 2006.12.14-17. : ., ISBN 978-3-7643-8910-9, (2009), S. 207-235

Azizov, Tomas Ya.; Behrndt, Jussi; Philipp, Friedrich; Trunk, Carsten
On domains of powers of linear operators and finite rank perturbations. - In: / Workshop on Operator Theory in Krein Spaces and Operator Polynomials ; 6 (Berlin) : 2006.12.14-17. : ., ISBN 978-3-7643-8910-9, (2009), S. 31-36

Behrndt, Jussi; Förster, Karl-Heinz; Langer, Heinz; Trunk, Carsten
Spectral theory in inner product spaces and applications : 6th Workshop on Operator Theory in Krein Spaces and Operator Polynomials, Berlin, December 2006. - Basel [u.a.] : Birkhäuser. - XX, 250 S.. - (Operator theory. - 188)
ISBN 3764389109 = 978-3-7643-8910-9
Literaturangaben
http://www.gbv.de/dms/ilmenau/toc/570513138.PDF
Trenn, Stephan
Distributional solution theory for linear DAEs. - In: Proceedings in applied mathematics and mechanics : PAMM. - Weinheim [u.a.] : Wiley-VCH, ISSN 16177061, Bd. 8 (2008), 1, S. 10077-10080
http://dx.doi.org/10.1002/pamm.200810077
Homburg, Ale Jan; Jukes, Alice C.; Knobloch, Jürgen; Lamb, Jeroen S. W.
Saddle-nodes and period-doublings of Smale horseshoes: a case study near resonant homoclinic bellows. - In: Bulletin of the Belgian Mathematical Society - Simon Stevin. - Brussels : Soc, Bd. 15 (2008), 5, S. 833-850
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Knobloch, Jürgen; Wagenknecht, Thomas
Snaking of multiple homoclinic orbits in reversible systems. - In: SIAM journal on applied dynamical systems. - Philadelphia, Pa : SIAM, ISSN 15360040, Bd. 7 (2008), 4, S. 1397-1420
http://dx.doi.org/10.1137/070695800
Jacob, Birgit; Trunk, Carsten; Winklmeier, Monika
Analyticity and Riesz basis property of semigroups associated to damped vibrations. - In: Journal of evolution equations : JEE. - Basel : Springer, ISSN 14243202, Bd. 8 (2008), 2, S. 263-281
http://dx.doi.org/10.1007/s00028-007-0351-6
Strauss, Vladimir A.; Trunk, Carsten
Spectralizable operators. - In: Integral equations and operator theory : IEOT. - Berlin : Springer, ISSN 14208989, Bd. 61 (2008), 3, S. 413-422
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Steigenberger, Joachim; Abeßer, Harald
Quasistatic inflation processes within rigid tubes. - In: ZAMM : journal of applied mathematics and mechanics. - Berlin : Wiley-VCH, ISSN 15214001, Bd. 88 (2008), 7, S. 556-572
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Trunk, Carsten
Spectral theory for operator matrices related to models in mechanics. - In: Mathematical notes. - Dordrecht [u.a.] : Springer Science + Business Media B.V, ISSN 15738876, Bd. 83 (2008), 5/6, S. 843-850
http://dx.doi.org/10.1134/S0001434608050295
Ilchmann, Achim; Mueller, Markus
Robustness of [lambda]-tracking in the gap metric. - In: SIAM journal on control and optimization. - Philadelphia, Pa : Soc, ISSN 10957138, Bd. 47 (2008), 5, S. 2724-2744
http://dx.doi.org/10.1137/07070142X
Trenn, Stephan
Multilayer perceptrons: approximation order and necessary number of hidden units. - In: IEEE transactions on neural networks : a publication of the IEEE Neural Networks Council. - New York, NY : IEEE, ISSN 19410093, Bd. 19 (2008), 5, S. 836-844
http://dx.doi.org/10.1109/TNN.2007.912306
Behrndt, Jussi; Katatbeh, Qutaibeh; Trunk, Carsten
Non-real eigenvalues of singular indefinite Sturm-Liouville operators. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 10 S., 250,5 KB). - (Preprint. - M08,28)
http://www.db-thueringen.de/servlets/DocumentServlet?id=11843
Trenn, Stephan
Regularity of distributional differential algebraic equations. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 36 S., 328,1 KB). - (Preprint. - M08,24)
http://www.db-thueringen.de/servlets/DocumentServlet?id=11764
Behrndt, Jussi; Katatbeh, Qutaibeh; Trunk, Carsten
Accumulation of complex eigenvalues of indefinite Sturm-Liouville operators. - In: Journal of physics / A. - Bristol : IOP Publ, ISSN 17518121, Bd. 41Bd. 41.2008, 24, 244003, insges. 10 S.
http://dx.doi.org/10.1088/1751-8113/41/24/244003
Krauskopf, Bernd; Rieß, Thorsten
A Lin's method approach to finding and continuing heteroclinic connections involving periodic orbits. - In: Nonlinearity : ... a journal of the Institute of Physics and the London Mathematical Society. - Bristol : IOP Publ, ISSN 13616544, Bd. 21 (2008), 8, S. 1655-1690
http://dx.doi.org/10.1088/0951-7715/21/8/001
Müller, Markus
Output feedback stabilization of multivariable systems with vector relative degree. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 21 S., 209,1 KB). - (Preprint. - M08,23)
http://www.db-thueringen.de/servlets/DocumentServlet?id=11608
Ilchmann, Achim; Ke, Zhenqing; Logemann, Hartmut
Indirect sampled-data control with sampling period adaptation. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 10 S., 209,2 KB). - (Preprint. - M08,22)
http://www.db-thueringen.de/servlets/DocumentServlet?id=11563
Rieß, Thorsten
A Lin's method approach to heteroclinic connections involving periodic orbits : analysis and numerics. - Online-Ressource (PDF-Datei: 134 S., 2071 KB)
Ilmenau : Techn. Univ., Diss., 2008

Die Dissertationsschrift beschäftigt sich mit der Bifurkationsanalyse von heteroklinen Zyklen, die eine hyperbolische Gleichgewichtslage und einen hyperbolischen periodischen Orbit miteinander verbinden. Im ersten Teil der Arbeit wird eine Erweiterung von Lins Methode entwickelt, die auf einer Kopplung des globalen kontinuierlichen Systems und des diskreten Systems, das die Dynamik in der Umgebung des periodischen Orbits beschreibt, beruht. Die Methode erlaubt es, Bifurkationsgleichungen für das gegebene Szenario zu formulieren. Die Bifurkationsgleichungen für homokline Orbits an die Gleichgewichtslage und homokline Orbits an den periodischen Orbit werden qualitativ gelöst und diskutiert, ebenso wird der Fall einer quadratischen Berührung behandelt. Im zweiten Teil der Dissertation wird auf Basis der theoretischen Ergebnisse eine numerische Methode entwickelt, die es erlaubt, verbindende Orbits zwischen Gleichgewichtslagen und periodischen Orbits zu finden und im Parameterraum zu verfolgen. Die Methode wird an drei ausgewählten Beispielen demonstriert, dabei werden die theoretischen Ergebnisse aus dem ersten Teil der Arbeit bestätigt. Eine Erweiterung der numerischen Methode auf verbindende Orbits zwischen zwei hyperbolischen periodischen Orbits wird abgeleitet.


http://www.db-thueringen.de/servlets/DerivateServlet/Derivate-14786/ilm1-2007000415.pdf
Ilchmann, Achim; Pham Huu Anh, Ngoc
Stability of positive linear Volterra integro-differential systems with delays. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 29 S., 324 KB). - (Preprint. - M08,21)
http://www.db-thueringen.de/servlets/DocumentServlet?id=11321
Jacob, Birgit; Trunk, Carsten
Spectrum and analyticity of semigroups arising in elasticity theory and hydromechanics. - Ilmenau : Techn. Univ., Inst. für Mathematik. - Online-Ressource (PDF-Datei: 20 S., 691 KB). - (Preprint. - M08,19)
http://www.db-thueringen.de/servets/DocumentServlet?id=11137
French, Mark; Ilchmann, Achim; Mueller, Markus
Robust stabilization by linear output delay feedback. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 25 S. = 340,3 KB, Text. - (Preprint. - M08,16)
http://www.db-thueringen.de/servlets/DocumentServlet?id=10859
Trunk, Carsten
Analyticity of semigroups related to a class of block operator matrices. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 15 S. = 245,8 KB, Text. - (Preprint. - M08,15)
http://www.db-thueringen.de/servlets/DocumentServlet?id=10740
Trenn, Stephan
Distributional solution theory for linear DAEs. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 4 S. = 170,61 KB, Text. - (Preprint. - M08,14)
http://www.db-thueringen.de/servlets/DocumentServlet?id=10616
Ilchmann, Achim; Ryan, Eugene P.
Performance funnels and tracking control. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 21 S. = 349,1 KB, Text. - (Preprint. - M08,13)
http://www.db-thueringen.de/servlets/DocumentServlet?id=10615
Azizov, Tomas Ya.; Behrndt, Jussi; Jonas, Peter; Trunk, Carsten
Spectral points of definite type and type π for linear operators and relations in Krein spaces. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 29 S. = 311,6 KB, Text. - (Preprint. - M08,12)
http://www.db-thueringen.de/servlets/DocumentServlet?id=10405
Philipp, Friedrich; Trunk, Carsten
G-selfadjoint operators in Almost Pontryagin spaces. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 29 S. = 330,1 KB, Text. - (Preprint. - M08,08)
http://www.db-thueringen.de/servlets/DocumentServlet?id=10383
Ilchmann, Achim; Pham Huu Anh, Ngoc
On positivity and stability of linear time-varying Volterra equations. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 10 S. = 226,7 KB, Text. - (Preprint. - M08,05)
http://www.db-thueringen.de/servlets/DocumentServlet?id=10377
Müller, Markus
Normal form for linear systems with respect to its vector relative degree. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 21 S. = 259,4 KB, Text. - (Preprint. - M08,04)
http://www.db-thueringen.de/servlets/DocumentServlet?id=10375
Azizov, Tomas Ya.; Jonas, Peter; Trunk, Carsten
Small perturbation of selfadjoint and unitary operators in Krein spaces. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 12 S. = 246,6 KB, Text. - (Preprint. - M08,03)
http://www.db-thueringen.de/servlets/DocumentServlet?id=9918
Azizov, Tomas Ya.; Behrndt, Jussi; Trunk, Carsten
On finite rank perturbations of definitizable operators. - In: Journal of mathematical analysis and applications. - Amsterdam [u.a.] : Elsevier, Bd. 339 (2008), 2, S. 1161-1168
http://dx.doi.org/10.1016/j.jmaa.2007.07.016
Ilchmann, Achim; Ryan, Eugene P.; Townsend, Philip
Tracking with prescribed transient behavior for nonlinear systems of known relative degree. - In: SIAM journal on control and optimization. - Philadelphia, Pa : Soc, ISSN 10957138, Bd. 46 (2007), 1, S. 210-230
http://dx.doi.org/10.1137/050641946
Caraballo, Tomás; Crauel, Hans; Langa, José A.; Robinson, James C.
The effect of noise on the Chafee-Infante equation : a nonlinear case study. - In: Proceedings of the American Mathematical SocietyProceedings of the American Mathematical Society. - Providence, RI : Soc - Providence, RI : Soc., ISSN 00029939, Bd. 135 (2007), 2, S. 373-382
Jacob, Birgit; Morris, Kirsten; Trunk, Carsten
Minimum-phase infinite-dimensional second-order systems. - In: IEEE transactions on automatic control. - New York, NY : Institute of Electrical and Electronics Engineers, ISSN 15582523, Bd. 52 (2007), 9, S. 1654-1665
http://dx.doi.org/10.1109/TAC.2007.904471
Naito, Toshiki; Shin, Jong Son; Murakami, Satoru; Pham Huu Anh, Ngoc
Characterizations of linear Volterra integral equations with nonnegative kernels. - In: Journal of mathematical analysis and applications. - Amsterdam [u.a.] : Elsevier, Bd. 335 (2007), 1, S. 298-313
http://dx.doi.org/10.1016/j.jmaa.2007.01.070
Crauel, Hans; Damm, Tobias; Ilchmann, Achim
Stabilization of linear systems by rotation. - In: Journal of differential equations. - Orlando, Fla : Elsevier, ISSN 10902732, Bd. 234 (2007), 2, S. 412-438
http://dx.doi.org/10.1016/j.jde.2006.12.005
Jonas, Peter; Trunk, Carsten
A Sturm-Liouville problem depending rationally on the eigenvalue parameter. - In: Mathematische Nachrichten. - [S.l.] : Wiley-VCH, ISSN 15222616, Bd. 280 (2007), 15, S. 1709-1726
http://dx.doi.org/10.1002/mana.200510573
Pham Huu Anh, Ngoc
Stability radii of positive linear Volterra-Stieltjes equations. - In: Journal of differential equations. - Orlando, Fla : Elsevier, ISSN 10902732, Bd. 243 (2007), 1, S. 101-122
http://dx.doi.org/10.1016/j.jde.2007.08.005
Trenn, Stephan
A normal form for pure differential algebraic systems. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 18 S. = 216,4 KB, Text. - (Preprint. - M08,01)
http://www.db-thueringen.de/servlets/DocumentServlet?id=9802
Trenn, Stephan
Multilayer perceptrons: approximation order and necessary number of hidden units. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 9 S. = 291,1 KB, Text. - (Preprint. - M07,27)
http://www.db-thueringen.de/servlets/DocumentServlet?id=9800
Azizov, Tomas Ya.; Behrndt, Jussi; Jonas, Peter; Trunk, Carsten
Compact and finite rank perturbations of linear relations in Hilbert spaces. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 13 S. = 248,7 KB, Text. - (Preprint. - M07,25)
http://www.db-thueringen.de/servlets/DocumentServlet?id=9797
Strauss, Vladimir A.; Trunk, Carsten
Spectralizable operators. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 10 S. = 285,5 KB, Text. - (Preprint. - M07,24)
http://www.db-thueringen.de/servlets/DocumentServlet?id=9795
Karabash, Illya; Trunk, Carsten
Spectral properties of singular Sturm-Liouville operators with indefinite weight sgn x. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 20 S. = 326,2 KB, Text. - (Preprint. - M07,23)
http://www.db-thueringen.de/servlets/DocumentServlet?id=9794
Behrndt, Jussi; Katatbeh, Qutaibeh; Trunk, Carsten
Accumulation of complex eigenvalues of indefinite Sturm-Liouville operators. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 12 S. = 272,9 KB, Text. - (Preprint. - M07,22)
http://www.db-thueringen.de/servlets/DocumentServlet?id=9793
Azizov, Tomas Ya.; Behrndt, Jussi; Philipp, Friedrich; Trunk, Carsten
On domains of powers of linear operators and finite rank perturbations. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 6 S. = 141,65 KB, Text. - (Preprint. - M07,21)
http://www.db-thueringen.de/servlets/DocumentServlet?id=9787
Trunk, Carsten
Spectral theory for operator matrices related to models in mechanics. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 12 S. = 203,3 KB, Text. - (Preprint. - M07,20)
http://www.db-thueringen.de/servlets/DocumentServlet?id=9785
Jacob, Birgit; Trunk, Carsten; Winklmeier, Monika
Analyticity and Riesz basis property of semigroups associated to damped vibrations. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 20 S. = 285,5 KB, Text. - (Preprint. - M07,19)
http://www.db-thueringen.de/servlets/DocumentServlet?id=9783
Trunk, Carsten
Perturbation theory for self-adjoint operators in Krein spaces. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 12 S. = 206,6 KB, Text. - (Preprint. - M07,18)
http://www.db-thueringen.de/servlets/DocumentServlet?id=9782
Strauss, Vladimir A.; Trunk, Carsten
Some Sobolev spaces as Pontryagin spaces. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 14 S. = 239,8 KB, Text. - (Preprint. - M07,17)
http://www.db-thueringen.de/servlets/DocumentServlet?id=9781
Ilchmann, Achim; Mueller, Markus
Robustness of [lambda]-tracking in the gap metric. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 19 S. = 285,9 KB, Text. - (Preprint. - M07,13)
http://www.db-thueringen.de/servlets/DocumentServlet?id=9400
Ilchmann, Achim; Mueller, Markus
Time-varying linear systems: relative degree and normal form. - In: IEEE transactions on automatic control. - New York, NY : Institute of Electrical and Electronics Engineers, ISSN 15582523, Bd. 52 (2007), 5, S. 840-851
http://dx.doi.org/10.1109/TAC.2007.895843
Ilchmann, Achim; Schuster, Hans
PI-funnel control for two mass systems. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 18 S. = 438,2 KB. - (Preprint. - M07,02)
http://www.db-thueringen.de/servlets/DocumentServlet?id=8314
Ilchmann, Achim; Logemann, Hartmut; Ryan, Eugene P.
Tracking with prescribed transient performance for hysteretic systems. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 20 S. = 347,0 KB. - (Preprint. - M07,01)
http://www.db-thueringen.de/servlets/DocumentServlet?id=8312
Knobloch, Jürgen
Chaotic behaviour near non-transversal homoclinic points with quadratic tangency. - In: Journal of difference equations and applications. - London [u.a.] : Taylor & Francis, ISSN 15635120, Bd. 12 (2006), 10, S. 1037-1056
http://dx.doi.org/10.1080/10236190600986644
Ilchmann, Achim; Logemann, Hartmut; Ryan, Eugene P.
Tracking with prescribed transient behaviour for a class of nonlinear functional differential equations with input hysteresis. - In: 45th IEEE Conference on Decision and Control, 2006 : 13 - 15 Dec. 2006, [San Diego, CA, USA]. - Piscataway, NJ : IEEE Service Center / IEEE Conference on Decision and Control ; 45 (San Diego, Calif.) : 2006.12.13-15., (2006), S. 3089-3092

http://dx.doi.org/10.1109/CDC.2006.377663
French, Mark; Ilchmann, Achim; Ryan, Eugene P.
Robustness in the graph topology of a common adaptive controller. - In: SIAM journal on control and optimization. - Philadelphia, Pa : Soc, ISSN 10957138, Bd. 45 (2006), 5, S. 1736-1757
http://dx.doi.org/10.1137/0506336371
Mandaloju, Nagendra P.; Trenn, Stephan
Analogue implementation of the funnel controller. - In: Proceedings in applied mathematics and mechanics : PAMM. - Weinheim [u.a.] : Wiley-VCH, ISSN 16177061, Bd. 6 (2006), 1, S. 823-824
http://dx.doi.org/10.1002/pamm.200610391
Ilchmann, Achim; Sawodny, Oliver; Trenn, Stephan
Pneumatic cylinders: modelling and feedback force-control. - In: International journal of control. - London : Taylor & Francis, ISSN 13665820, Bd. 79 (2006), 6, S. 650-661
http://dx.doi.org/10.1080/00207170600645875
Ilchmann, Achim; Ryan, Eugene P.
Asymptotic tracking with prescribed transient behaviour for linear systems. - In: International journal of control. - London : Taylor & Francis, ISSN 13665820, Bd. 79 (2006), 8, S. 910-917
http://dx.doi.org/10.1080/00207170600708699
Klaus, Jenny
Bifurcations from homoclinic orbits to a saddle-centre in reversible systems. - Online-Ressource (PDF-Datei: 146 S:, 1369 KB)
Ilmenau : Techn. Univ., Diss., 2006

In der Dissertation werden Bifurkationen homokliner Orbits zu einem Sattel-Zentrum in reversiblen Systemen betrachtet. Das Sattel-Zentrum wird durch ein Paar rein imaginärer Eigenwerte generiert, der Rest des Spektrums besteht aus Eigenwerten mit einem von Null verschiedenen Realteil. Somit ist die zweidimensionale Zentrumsmannigfaltigkeit mit einer Familie symmetrischer, periodischer Orbits ausgefüllt. In der Dissertation wurde Lin's Methode auf den Fall nicht hyperbolischer Gleichgewichtslagen erweitert. Ursprünglich wurde diese Methode für Untersuchungen des Bifurkationsverhaltens von Orbits, welche hyperbolische Gleichgewichtslagen verbinden, entwickelt. Zuerst werden in der Dissertation 1-homokline Orbits zur Zentrumsmannigfaltigkeit betrachtet. Dabei werden 1-homokline Orbits zur Gleichgewichtslage, 1-homokline Orbits zu periodischen Orbits der Zentrumsmannigfaltigkeit und heterokline Orbits, die verschiedene Orbits der Zentrumsmannigfaltigkeit verbinden, unterschieden. Ein zweiter Aspekt der Dissertation ist die Detektion von verzweigenden symmetrischen, 1-periodischen Orbits. Dabei dienen die verzweigenden 1-Homoklinen zur Zentrumsmannigfaltigkeit als Basis für die Diskussion der zugehörigen Verzweigungsgleichungen.


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Duc, Luu Hoang; Ilchmann, Achim; Siegmund, Stefan; Taraba, Peter
On stability of linear time-varying second-order differential equations. - In: Quarterly of applied mathematics. - Providence, RI : Brown University, Division of Applied Mathematics, ISSN 15524485, Bd. 64 (2006), 1, S. 137-151
http://dx.doi.org/10.1090/S0033-569X-06-00995-X
Ilchmann, Achim; Ryan, Eugene P.
Adaptive and non-adaptive control without identification : a survey. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 10 S. = 174,0 KB, Text. - (Preprint. - M06,10)
http://www.db-thueringen.de/servlets/DocumentServlet?id=6709
Steigenberger, Joachim; Abeßer, Harald
Quasistatic inflation processes within rigid tubes. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 37 S. = 655,4 KB. - (Preprint. - M06,09)
http://www.db-thueringen.de/servlets/DocumentServlet?id=6541
Crauel, Hans
Measure attractors and Markov attractors. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 31 S. = 286,9 KB. - (Preprint. - M06,08)
http://www.db-thueringen.de/servlets/DocumentServlet?id=6254
Ilchmann, Achim; Ryan, Eugene P.; Townsend, Philip
Tracking control with prescribed transient behaviour for systems of known relative degree. - In: Systems & control letters. - Amsterdam [u.a.] : Elsevier, ISSN 18727956, Bd. 55 (2006), 5, S. 396-406
http://dx.doi.org/10.1016/j.sysconle.2005.09.002
Ilchmann, Achim; Ryan, Eugene P.; Townsend, Philip
Tracking control with prescribed transient behaviour for systems of known relative degree. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 21 S. = 348,8 KB. - (Preprint. - M05,02)
http://www.db-thueringen.de/servlets/DocumentServlet?id=5375
Duc, Luu Hoang; Ilchmann, Achim; Siegmund, Stefan; Taraba, Peter
On stability of linear time-varying second-order differential equations. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 17 S. = 215,4 KB. - (Preprint. - M05,03)
http://www.db-thueringen.de/servlets/DocumentServlet?id=5376
Ilchmann, Achim; Sawodny, Oliver; Trenn, Stephan
Pneumatic cylinders: modelling and feedback force-control. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 22 S. = 475,1 KB. - (Preprint. - M05,05)
http://www.db-thueringen.de/servlets/DocumentServlet?id=5378
Ilchmann, Achim; Ryan, Eugene P.
Asymptotic tracking with prescribed transient behaviour for linear systems. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 15 S. = 250,4 KB. - (Preprint. - M05,06)
http://www.db-thueringen.de/servlets/DocumentServlet?id=5379
French, Mark; Ilchmann, Achim; Ryan, Eugene P.
Robustness in the graph topology of a common adaptive controller. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 27 S. = 367,5 KB. - (Preprint. - M05,10)
http://www.db-thueringen.de/servlets/DocumentServlet?id=5377
Abeßer, Harald; Steigenberger, Joachim
Optimalsteuerprobleme unter Zustandsrestriktionen. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 44 S. = 431,3 KB. - (Preprint. - M05,11)
http://www.db-thueringen.de/servlets/DocumentServlet?id=5481
Crauel, Hans; Damm, Tobias; Ilchmann, Achim
Stabilization of linear systems by rotation. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 26 S. = 375 KB. - (Preprint. - M05,18)
http://www.db-thueringen.de/servlets/DocumentServlet?id=5390
Caraballo, Tomás; Crauel, Hans; Langa, José A.; Robinson, James C.
The effect of noise on the Chaffee-Infante equation : a nonlinear case study. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 11 S. = 165,7 KB. - (Preprint. - M05,16)
http://www.db-thueringen.de/servlets/DocumentServlet?id=5427
Ilchmann, Achim; Mueller, Markus
Time-varying linear systems: relative degree and normal form. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 21 S. = 249,5 KB. - (Preprint. - M05,15)
http://www.db-thueringen.de/servlets/DocumentServlet?id=5392
Ilchmann, Achim; Ryan, Eugene P.; Townsend, Philip
Tracking with prescribed transient behaviour for nonlinear systems of known relative degree. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 21 S. = 423,3 KB. - (Preprint. - M05,14)
http://www.db-thueringen.de/servlets/DocumentServlet?id=5428
Ilchmann, Achim; Logemann, Hartmut; Ryan, Eugene P.
Output tracking with prescribed transient behaviour for linear systems with input hysteresis. - 9 S. = 474,7 KB, Text
Druckausg.: Modeling and control of autonomous decision support based systems : proceedings of the 13th International Workshop on Dynamics & Control held in Wiesensteig, Germany, May 22 - 26, 2005. - Aachen : Shaker, 2005, ISBN 3-8322-3962-6, S. 271-278
http://www.db-thueringen.de/servlets/DocumentServlet?id=5577
French, Mark; Trenn, Stephan
l p gain bounds for switched adaptive controllers. - 6 S. = 260,8 KB, Text
Druckausg.: 2005 44th IEEE Conference on Decision and Control & European Control Conference : Seville, Spain, 12 - 15 December 2005. - Piscataway, NJ : IEEE Operations Center, 2005. - Vol. 3, S. 2865-2870

A class of discrete plants controlled by a switching adaptive strategy is considered, and l p bounds, 1 ≤ p ≤ ∞, are obtained for the closed loop gain relating input and output disturbances to internal signals.


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Crauel, Hans; Damm, Tobias; Ilchmann, Achim
Stabilization of linear systems by dynamic high-gain rotation. - 6 S. = 196,3 KB, Text
CD-ROM-Ausg.: Preprints of the 16th World Congress of the International Federation of Automatic Control : July 3 - 8, 2005, Prague, Czech Republic/ ed. by Petr Horacek ..... - [S.l.] : IFAC, 2005. - insges. 6 S.
http://www.db-thueringen.de/servlets/DocumentServlet?id=5396
Ilchmann, Achim
Algebraic theory of time-varying linear systems : a survey. - 8 S. = 174,3 KB, Text
CD-ROM-Ausg.: Preprints of the 16th World Congress of the International Federation of Automatic Control : July 3 - 8, 2005, Prague, Czech Republic / ed. by Petr Horacek ... - [S.l.] : IFAC, 2005. - insges. 7 S.
http://www.db-thueringen.de/servlets/DocumentServlet?id=5395
Ilchmann, Achim; Townley, Stuart; Thuto, Mosalagae
Adaptive sampled-data tracking for input-constrained exothermic chemical reaction models. - In: Systems & control letters. - Amsterdam [u.a.] : Elsevier, ISSN 18727956, Bd. 54 (2005), 12, S. 1149-1161
http://dx.doi.org/10.1016/j.sysconle.2005.04.004
Ilchmann, Achim; Mehrmann, Volker
A behavioral approach to time-varying linear systems : part 2: descriptor systems. - In: SIAM journal on control and optimization. - Philadelphia, Pa : Soc, ISSN 10957138, Bd. 44 (2005), 5, S. 1748-1765
http://dx.doi.org/10.1137/040609021
Ilchmann, Achim; Mehrmann, Volker
A behavioral approach to time-varying linear systems : part 1: general theory. - In: SIAM journal on control and optimization. - Philadelphia, Pa : Soc, ISSN 10957138, Bd. 44 (2005), 5, S. 1725-1747
http://dx.doi.org/10.1137/S0363012904442239
Homburg, Ale Jan; Knobloch, Jürgen
Bellows bifurcating from degenerate homoclinic orbits in conservative systems. - In: / International Conference on Differential Equations (Hasselt/Diepenbeek) : 2003.07.22-26. : ., ISBN 978-981-256-169-5, (2005), S. 963-971

Knobloch, Jürgen; Wagenknecht, Thomas
Homoclinic snaking near a heteroclinic cycle in reversible systems. - In: Physica / D. - Amsterdam [u.a.] : Elsevier, ISSN 18728022, Bd. 206 (2005), 1/2, S. 82-93
http://dx.doi.org/10.1016/j.physd.2005.04.018
Ilchmann, Achim; Ryan, Eugene P.; Trenn, Stephan
Tracking control: performance funnels and prescribed transient behaviour. - In: Systems & control letters. - Amsterdam [u.a.] : Elsevier, ISSN 18727956, Bd. 54 (2005), 7, S. 655-670
http://dx.doi.org/10.1016/j.sysconle.2004.11.005
Ilchmann, Achim; Townley, Stuart; Thuto, Mosalagae
Adaptive sampled-data tracking for input constrained exothermic chemical reaction models. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 17 S. = 339 KB. - (Preprint. - M04,18)
http://www.db-thueringen.de/servlets/DocumentServlet?id=5608
Ilchmann, Achim; Mehrmann, Volker
A behavioural approach to linear time-varying descriptor systems. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 24 S. = 229,2 KB. - (Preprint. - M04,11)
http://www.db-thueringen.de/servlets/DocumentServlet?id=5655
Crauel, Hans; Duc, Luu Hoang; Siegmund, Stefan
Towards a morse theory for random dynamical systems. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 22 S. = 309,9 KB. - (Preprint. - M04,10)
http://www.db-thueringen.de/servlets/DocumentServlet?id=5662
Ilchmann, Achim; Ryan, Eugene P.; Trenn, Stephan
Tracking control: performance funnels and prescribed transient behaviour. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 23 S. = 231,6 KB. - (Preprint. - M04,08)
http://www.db-thueringen.de/servlets/DocumentServlet?id=5663
Ilchmann, Achim; Mehrmann, Volker
A behavioural approach to time-varying linear systems. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 26 S. = 297,9 KB. - (Preprint. - M04,07)
http://www.db-thueringen.de/servlets/DocumentServlet?id=5665
Ilchmann, Achim; Ryan, Eugene P.; Trenn, Stephan
Adaptive tracking within prescribed funnels. - 6 S. = 294,7 KB, Text
Druckausg.: Proceedings of the 2004 IEEE International Conference on Control Applications : September 2 - 4, 2004, the Grand Hotel, Taipei, Taiwan; [joint the IEEE International Symposium on Intelligent Control (ISIC '04) and the IEEE International Symposium on Computer Aided Control Systems Design (CACSD '04)] / sponsored by the IEEE Control Systems Society. Hosted by Ministry of Education, Taiwan, R.O.C. ... ; Vol. 2, S. 1032-1036
http://www.db-thueringen.de/servlets/DocumentServlet?id=4246
Ilchmann, Achim; Thuto, Mosalagae; Townley, Stuart
Input constrained adaptive tracking with applications to exothermic chemical reactions models. - In: SIAM journal on control and optimization. - Philadelphia, Pa : Soc, ISSN 10957138, Bd. 43 (2004), 1, S. 154-173
. - 21 S. = 1,18 MB Text
http://dx.doi.org/10.1137/S0363012901391081
Ilchmann, Achim; Sangwin, C. J.
Output feedback stabilisation of minimum phase systems by delays. - In: Systems & control letters. - Amsterdam [u.a.] : Elsevier, ISSN 18727956, Bd. 52 (2004), 3/4, S. 233-245
http://dx.doi.org/10.1016/j.sysconle.2004.02.001
Ilchmann, Achim; Trenn, Stephan
Input constrained funnel control with applications to chemical reactor models. - In: Systems & control letters. - Amsterdam [u.a.] : Elsevier, ISSN 18727956, Bd. 53 (2004), 5, S. 361-375
http://dx.doi.org/10.1016/j.sysconle.2004.05.014
Ilchmann, Achim; Ryan, Eugene P.
On tracking and disturbance rejection by adaptive control. - In: Systems & control letters. - Amsterdam [u.a.] : Elsevier, ISSN 18727956, Bd. 52 (2004), 2, S. 137-147
http://dx.doi.org/10.1016/j.sysconle.2003.11.007
Knobloch, Jürgen
Lin's method for discrete and continuous dynamical systems and applications. - III, 197 Bl
Ilmenau : Techn. Univ., Habil.-Schr., 2004
Klaus, Jenny; Knobloch, Jürgen
Bifucation of homoclinic orbits to a saddle-center in reversible systems. - In: International journal of bifurcation and chaos (IJBC) : in applied sciences and engineering. - [Singapore] : World Scientific, Bd. 13 (2003), 9, S. 2603-2622
http://dx.doi.org/10.1142/S0218127403008119
Crauel, Hans; Matsikis, Iakovos; Townley, Stuart
Noise assisted high-gain stabilization: almost surely or in second mean. - In: SIAM journal on control and optimization. - Philadelphia, Pa : Soc, ISSN 10957138, Bd. 42 (2003), 5, S. 1834-1853
http://dx.doi.org/10.1137/S0363012901393900
Wagenknecht, Thomas; Champneys, A. R.
When gap solitons become embedded solitons: a generic unfolding. - In: Physica / D. - Amsterdam [u.a.] : Elsevier, ISSN 18728022, Bd. 177 (2003), 1/4, S. 50-70
http://dx.doi.org/10.1016/S0167-2789(02)00773-X
Ilchmann, Achim; Ryan, Eugene P.
On gain adaptation in adaptive control. - In: IEEE transactions on automatic control. - New York, NY : Institute of Electrical and Electronics Engineers, ISSN 15582523, Bd. 48 (2003), 5, S. 895-899
http://dx.doi.org/10.1109/TAC.2003.811276
Wagenknecht, Thomas
Homoclinic bifurcations in reversible systems. - Online-Ressource (PDF-Datei: 138 S., 964 KB)
Ilmenau : Techn. Univ., Diss., 2003

Die vorliegende Arbeit untersucht Bifurkationen homokliner Lösungen in gewöhnlichen Differentialgleichungen. Homokline Lösungen sind in positiver und negativer Zeit asymptotisch zu einer Gleichgewichtslage, d.h. zu einer konstanten Lösung der Differentialgleichung. Die Arbeit betrachtet solche homokline Bifurkationen, die von einer Veränderung des Typs dieser assoziierten Gleichgewichtslage herrühren. Verschiedene Szenarien werden in der Klasse der reversiblen Differentialgleichungen analysiert. - Der Hauptteil der Arbeit beschäftigt sich mit Homoklinen an Gleichgewichtslagen, welche selbst in einer lokalen Bifurkation verzweigen. Dabei verändert sich der Typ der Gleichgewichtslage vom reellen Sattel (mit führenden reellen Eigenwerten) zum Sattel-Zentrum (mit einem Paar rein imaginärer Eigenwerte). Das Miteinander lokaler und globaler Bifurkationseffekte erfordert eine neuartige Behandlung: Durch eine Kombination analytischer und geometrischer Techniken wird eine Beschreibung verzweigender Homoklinen gewonnen. Dabei werden sowohl rein reversible Systeme als auch Systeme mit zusätzlicher Symmetrie und Hamilton-Struktur betrachtet. - Im zweiten Teil der Arbeit werden homokline Bifurkationsphänomene untersucht, die von einer Typveränderung der Gleichgewichtslage von rellem Sattel zu komplexem Sattel- Fokus (mit komplexen führenden Eigenwerten) herrühren. Dabei wird die Existenz von zwei Ausgangshomoklinen in sogenannter Blasebalg-Konfiguration (homoclinic bellows configuration) vorausgesetzt. Unter Verwendung einer auf Lin zurückgehenden analytischen Methode werden Bifurkationsresultate für verzweigende N-Homoklinen erzielt. - Die allgemeinen Bifurkationsresultate werden auf physikalische Probleme der nichtlinearen Optik und Wasserwellentheorie, sowie auf zwei mathematische Modellgleichungen angewendet und in numerischen Untersuchungen bestätigt.


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Zimmermann, Klaus; Gerlach, Erik; Jianjun, Huang; Behn, Carsten; Siebenhaar, C.
Simulation von biologisch-inspirierten Antrieben. - In: / ISOM 2002 ; 1 (Chemnitz) : 2002.03.21-22. : ., (2002), S. 483-491

Abeßer, Harald; Behn, Carsten; Steigenberger, Joachim; Zimmermann, Klaus
Steueraufgaben für Zweiarm-Roboter mit muskelähnlichen Antrieben. - In: / Internationales Wissenschaftliches Kolloquium. Technische Universität Ilmenau ; 47 (Ilmenau) : 2002.09.23-26., (2002), insges. 21 S.
Crauel, Hans
A uniformly exponential random forward attractor which is not a pullback attractor. - In: Archiv der Mathematik : ADM. - Basel : Birkhäuser, ISSN 14208938, Bd. 78 (2002), 4, S. 329-336
http://dx.doi.org/10.1007/s00013-002-8254-9
Crauel, Hans
Invariant measures for random dynamical systems on the circle. - In: Archiv der Mathematik : ADM. - Basel : Birkhäuser, ISSN 14208938, Bd. 78 (2002), 2, S. 145-154
http://dx.doi.org/10.1007/s00013-002-8228-y
Ilchmann, Achim; de Pinho, Maria do Rosário
Weak maximum principle for optimal control problems with mixed constraints. - In: Nonlinear analysis / Theory, methods and applications. - Amsterdam [u.a.] : Elsevier, Pergamon Press, ISSN 18735215, Bd. 48 (2002), 8, S. 1179-1196
http://dx.doi.org/10.1016/S0362-546X(01)00094-3
Ilchmann, Achim; Isidori, A.
Adaptive dynamic output feedback stabilisation of nonlinear systems. - 9 S. = 373,7 KB, Text
Druckausg.: Asian journal of control. - Xinzhu : Xuehui, ISSN 1561-8625, Bd. 4 (2002), S. 1-9
http://www.db-thueringen.de/servlets/DocumentServlet?id=4211
Ilchmann, Achim; Ryan, Eugene P.; Sangwin, Christopher J.
Tracking with prescribed transient behaviour. - In: Control, optimisation and calculus of variations : COCV. - Les Ulis : EDP Sciences, ISSN 12623377, Bd. 7 (2002), S. 471-493
http://dx.doi.org/10.1051/cocv:2002064
Ilchmann, Achim; Ryan, Eugene P.; Sangwin, C. J.
Systems of controlled functional differential equations and adaptive tracking. - In: SIAM journal on control and optimization. - Philadelphia, Pa : Soc, ISSN 10957138, Bd. 40 (2002), 6, S. 1746-1764
http://dx.doi.org/10.1137/S0363012900379704
Thomaschewski, Boris
Workspaces of continuous robotic manipulators. - Online-ressource (PDF-Datei: 109 S., 6485 KB)
Ilmenau : Techn. Univ., Diss., 2002
http://www.db-thueringen.de/servlets/DocumentServlet?id=1172
Crauel, Hans
Random probability measures on Polish spaces. - London [u.a.] : Taylor & Francis. - XVI, 118 S. - (Stochastics monographs. - 11)
ISBN 0415273870
Includes index
http://www.gbv.de/dms/goettingen/346993067.pdf
Crauel, Hans
Keller, Gerhard : Equilibrium states in ergodic theory : Cambridge [u.a.], Cambridge Univ. Press, 1998. - In: Bulletin of the London Mathematical Society. - Hoboken, NJ : Wiley, ISSN 14692120, 5, S. 636-637
Rezension von : Equilibrium states in ergodic theory / Keller, Gerhard. - Cambridge [u.a.] : Cambridge Univ. Press, 1998. - IX, 178 S.. - London Mathematical Society student texts ; 42. - Literaturverz. S. [169] - 173
http://dx.doi.org/10.1112/S002460930124853X
Crauel, Hans
Random point attractors versus random set attractors. - In: Journal of the London Mathematical Society. - Oxford : Wiley, ISSN 14697750, Bd. 63 (2001), 2, S. 413-427
http://dx.doi.org/10.1017/S0024610700001915
Knobloch, Jürgen
Chaotic behaviour near non-transversal homoclinic points with quadratic tangencies
Rev. version. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 22 S. = 345,4 KB. - (Preprint. - M00,07)
http://www.db-thueringen.de/servlets/DocumentServlet?id=6206
Crauel, Hans; Matsikis, Iakovos; Townley, Stuart
Noise assisted high-gain stabiblization: almost surely or in second mean. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 23 S. = 338,8 KB. - (Preprint. - M01,10)
http://www.db-thueringen.de/servlets/DocumentServlet?id=6028
Ilchmann, Achim; Ryan, Eugene P.; Sangwin, Christopher J.
Tracking with prescribed transient behaviour. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 25 S. = 1.24 MB. - (Preprint. - M01,16)
http://www.db-thueringen.de/servlets/DocumentServlet?id=5996
Ilchmann, Achim; Thuto, Mosalagae; Townley, Stuart
[lambda]-tracking for exothermic chemical reactions with saturating inputs. - 6 S. = 362,1 KB, Text
CD-ROM-Ausg.: Proceedings // European Control Conference, ECC '01 : 4 - 7 September 2001, Porto, Portugal / ed.: J. L. Martins de Carvalho ... - Porto, 2001, S. 1928-1933
http://www.db-thueringen.de/servlets/DocumentServlet?id=4656
de Pinho, Maria do Rosário; Ilchmann, Achim
On optimality conditions for optimal control problems with mixed constraints. - 6 S. = 129,3 KB, Text
CD-ROM-Ausg.: Proceedings // European Control Conference, ECC 2001 : 4-7 September 2001, Porto, Portugal / ed.: J. L. Martins de Carvalho. - Porto, 2001, S. 260-265
http://www.db-thueringen.de/servlets/DocumentServlet?id=4657
Ilchmann, Achim; Ryan, Eugene P.; Sangwin, Christopher J.
Adaptive tracking for systems described by functional differential equations. - 5 S. = 130,4 KB, Text
CD-ROM-Ausg.: Proceedings // European Control Conference, ECC 2001 : 4-7 September 2001, Porto, Portugal / ed.: J. L. Martins de Carvalho. - Porto, 2001, S. 2443-2447
http://www.db-thueringen.de/servlets/DocumentServlet?id=4654
Crauel, Hans
Uniform Lyapunov exponents are realised by ergodic invariant measures. - In: Stochastics and dynamics : SD. - Singapore [u.a.] : World Scientific, ISSN 02194937, Bd. 1 (2001), 1, S. 113-126
http://dx.doi.org/10.1142/S0219493701000072
Georgieva, Petia; Ilchmann, Achim; Weirig, Marie-France
Modelling and adaptive control of aerobic continuous stirred tank reactors. - 16 S. = 432,4 KB, Text
Druckausg.: European journal of control. - Paris : Hermes, ISSN 0947-3580, Bd. 7 (2001), 5, S. 476-491
http://www.db-thueringen.de/servlets/DocumentServlet?id=4212
Ilchmann, Achim
Dr&bovko;agan, Vasile; Halanay, Aristide : Stabilization of linear systems : Boston, Mass. [u.a.], Birkhäuser, 1999. - In: Automatica. - Amsterdam [u.a.] : Elsevier, Pergamon Press, ISSN 00051098, 5, S. 792-793
Rezension von : Stabilization of linear systems / Dr&bovko;agan, Vasile. - Boston, Mass. [u.a.] : Birkhäuser, 1999. - XIV, 308 S.. - System and control : Foundations & applications. - Literaturverz. S. 301 - 306
http://dx.doi.org/10.1016/S0005-1098(01)00018-8
Georgieva, Petia; Ilchmann, Achim
Adaptive [lambda]-tracking control of activated sludge processes. - In: International journal of control. - London : Taylor & Francis, ISSN 13665820, Bd. 74 (2001), 12, S. 1247-1259
. - Online-Ressource (PDF-Datei: 14 S., 2,7 MB)
http://dx.doi.org/10.1080/00207170110065910
Ilchmann, Achim; Mareels, Iven M. Y.
On stability radii of slowly time-varying systems. - 21 S. = 1,01 MB, Text
Druckausg.: Advances in mathematical systems theory : a volume in honor of Diederich Hinrichsen / Fritz Colonius ... ed., - Boston [u.a.] : Birkhäuser, 2001, S. 55-75
http://www.db-thueringen.de/servlets/DocumentServlet?id=4094
Knobloch, Jürgen
Lin's method for discrete dynamical systems. - In: Journal of difference equations and applications. - London [u.a.] : Taylor & Francis, ISSN 15635120, Bd. 6 (2000), 5, S. 577-623
http://dx.doi.org/10.1080/10236190008808247
Neundorf, Werner; Walther, Brigitte
Grafik, Animation und Ausgabeformate in Maple V Release 5. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 93 S. = 6,75 MB. - (Preprint. - M00,12)
http://www.db-thueringen.de/servlets/DocumentServlet?id=6032
Knobloch, Jürgen
Reduction of Hopf bifurcation problems with symmetries. - In: Bulletin of the Belgian Mathematical Society - Simon Stevin. - Brussels : Soc, Bd. 7 (2000), 2, S. 199-209
http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.bbms/1103055683
Crauel, Hans
White noise eliminates instability. - In: Archiv der Mathematik : ADM. - Basel : Birkhäuser, ISSN 14208938, Bd. 75 (2000), 6, S. 472-480
http://dx.doi.org/10.1007/s000130050532
Townley, Stuart; Ilchmann, Achim; Weiss, M. G.; Mcclements, W.; Ruiz, A. C.; Owens, D. H.; Prätzel-Wolters, D.
Existence and learning of oscillations in recurrent neural networks. - In: IEEE transactions on neural networks : a publication of the IEEE Neural Networks Council. - New York, NY : IEEE, ISSN 19410093, Bd. 11 (2000), 1, S. 205-214
. - 11 S. = 319 KB Text
http://dx.doi.org/10.1109/ACC.1997.611898 10.1109/72.822523
Steigenberger, Joachim
On a class of biomorphic motion systems. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 18 S. = 323,6 KB. - (Preprint. - M99,12)
http://www.db-thueringen.de/servlets/DocumentServlet?id=6095
Knobloch, Jürgen
Jump estimates for Lin's method. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 37 S. = 437,2 KB, Text. - (Preprint. - M99,31)
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Yin, Xianjun
On circular elastic rods as nonlinear springs and gripper elements. - In: / Internationales Wissenschaftliches Kolloquium. Technische Universität ; 44 (Ilmenau) : 1999.09.20-23. : ., (1999), S. 281-286
Thomaschewski, Boris; Abeßer, Harald; Steigenberger, Joachim
The workspace of a planar continuous robotic manipulator. - In: / Internationales Wissenschaftliches Kolloquium. Technische Universität ; 44 (Ilmenau) : 1999.09.20-23. : ., (1999), S. 322-326
Steigenberger, Joachim
On nonholonomic systems and biomorphic motion. - In: / Internationales Wissenschaftliches Kolloquium. Technische Universität ; 44 (Ilmenau) : 1999.09.20-23. : ., (1999), S. 216-219
Steigenberger, Joachim
Mathematical approach to worm-like locomotion. - In: Motion systems : proceedings of the First International Conference on Motion Systems, the Third Workshop of the Society of Technical Biology and Bionics and the Second Biomechanic Workshop of the Studygroup Morphology (DZG), Jena 1997. - Stuttgart [u.a.] : Fischer / International Conference on Motion Systems ; 1 (Jena) : 1997.09.29-30. : ., (1998), S. 114-115

Abeßer, Harald; Katzschmann, Michael; Steigenberger, Joachim
Time variant global stabilization of a mobile robot. - In: / International Conference in Honour of L. Bittner and R. Klötzler ; 12 (Trassenheide) : 1996.09.23-27. : ., (1998), S. 235-240

Knobloch, Jürgen
Bifurcation of degenerate homoclinic orbits in reversible and conservative systems. - In: Journal of dynamics and differential equations. - New York, NY [u.a.] : Springer Science + Business Media B.V, ISSN 15729222, Bd. 9 (1997), 3, S. 427-444
http://dx.doi.org/10.1007/BF02227489
Knobloch, Jürgen; Marx, Bernd; El Morsalani, Mohamed
Characterization of homoclinic points bifurcation from degenerate homoclinic orbits. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 14 S. = 184,1 KB, Text. - (Preprint. - M97,13)
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Steigenberger, Joachim; Zimmermann, Klaus; Petkun, Sergey
Modelle der Elastomechanik und ihre Anwendung in der Mikrotechnik. - In: / Internationales Wissenschaftliches Kolloquium. Technische Universität Ilmenau ; 41 (Ilmenau) : 1996.09.23-26. : ., (1996), S. 126-133
Steigenberger, Joachim
Classical framework for nonholonomic mechanical control systems. - In: International journal of robust and nonlinear control : IFAC affiliated journal. - New York, NY [u.a.] : Wiley, ISSN 10991239, Bd. 5 (1995), 4, S. 331-342
http://dx.doi.org/10.1002/rnc.4590050409
Schalk, Udo; Knobloch, Jürgen
Homoclinic points near degenerate homoclinics. - In: Nonlinearity : ... a journal of the Institute of Physics and the London Mathematical Society. - Bristol : IOP Publ, ISSN 13616544, Bd. 8 (1995), 6, S. 1133-1143
http://dx.doi.org/10.1088/0951-7715/8/6/014
Knobloch, Jürgen; Vanderbauwhede, André
Hopf bifurcation at k-fold resonances in reversible systems. - Ilmenau : Techn. Univ., Inst. für Mathematik. - 22 S. = 269,5 KB, Text. - (Preprint. - M95,16)
http://www.db-thueringen.de/servlets/DocumentServlet?id=6204
Schalk, Udo
Homokline Punkte in periodisch gestörten Systemen gewöhnlicher Differentialgleichungen. - II, 118 S.
Ilmenau : Techn. Univ., Diss., 1995
http://www.gbv.de/dms/ilmenau/toc/194472396.PDF
Steigenberger, Joachim; Fliegner, Thomas
Stability of a disturbance decoupled rigid body. - In: Systems & control letters. - Amsterdam [u.a.] : Elsevier, ISSN 18727956, Bd. 19 (1992), 3, S. 249-254
http://dx.doi.org/10.1016/0167-6911(92)90120-H
Vogel, Johannes
Foran, James : Fundamentals of real analysis : New York [u.a.], Dekker, 1991. - In: Ilmenauer Uni-Nachrichten. - Ilmenau, 15, S. 10
Rezension von : Fundamentals of real analysis / Foran, James. - New York, NY [u.a.] : Dekker, 1991. - XII, 473 S. - Pure and applied Mathematics ; 144. - Includes index
Vogel, Johannes
Geometry and complex variables, proceedings of an International Meeting on the Occasion of the IX Centennial of the University of Bologna, ed. by Salvatore Coen : New York, NY [u.a.], Dekker, 1991. - In: Ilmenauer Hochschulblatt. - Ilmenau, 10, S. 8
Rezension von : Geometry and complex variables : proceedings of an International Meeting on the Occasion of the IX Centennial of the University of Bologna / Coen, Salvatore. - New York, NY [u.a.] : Dekker, 1991. - XIII, 493 S. - Lecture notes in pure and applied mathematics ; 132. - Literaturangaben
Abesser, Harald; Steigenberger, Joachim
On structure preserving transformations in Hamiltonian control systems. - In: Zeitschrift für Analysis und ihre AnwendungenZeitschrift für Analysis und ihre Anwendungen. - Zürich : EMS Publishing House : . - Lemgo : Heldermann, ISSN 02322064, Bd. 10 (1991), 3, S. 319-333