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Winkler, Henrik; Woracek, Harald
Reparametrizations of non trace-normed Hamiltonians. - In: Spectral theory, mathematical system theory, evolution equations, differential and difference equations. - Basel : Birkhäuser, (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, 2012. - 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.



http://www.db-thueringen.de/servlets/DocumentServlet?id=20974
Philipp, Friedrich; Trunk, Carsten
The numerical range of non-negative operators in Krein spaces. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2012. - 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, (2012), S. 127-164

Berger, Thomas;
Robustness of stability of time-varying index-1 DAEs. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2012. - 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.



http://www.db-thueringen.de/servlets/DocumentServlet?id=20895
Berger, Thomas; Trenn, Stephan
Addition to: the quasi-Kronecker form for matrix pencils. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2012. - 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, 2012. - 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.



http://www.db-thueringen.de/servlets/DocumentServlet?id=20509
Ilchmann, Achim;
Decentralized tracking of interconnected systems. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2012. - 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].



http://www.db-thueringen.de/servlets/DocumentServlet?id=20508
Berger, Thomas; Halikias, George; Karcanias, Nicos
Effects of dynamic and non-dynamic element changes in RLC networks. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2012. - 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.



http://www.db-thueringen.de/servlets/DocumentServlet?id=20479
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