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Ilchmann, Achim; Selig, Tilman; Trunk, Carsten
The Byrnes-Isidori form for infinite-dimensional systems - Ilmenau : Techn. Univ., Inst. für Mathematik, 2013 - 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.



http://www.db-thueringen.de/servlets/DocumentServlet?id=23009
Hildenbrandt, Regina;
Partitions-requirements-matrices as optimal Markov kernels of special stochastic dynamic distance optimal partitioning problems. - In: International journal of pure and applied mathematics - Sofia : Academic Publications, ISSN 13118080, Bd. 88 (2013), 2, S. 183-211

The Stochastic Dynamic Distance Optimal Partitioning problem (SDDP problem) is a complex Operations Research problem. The SDDP problem is based on an industrial problem, which contains an optimal conversion of machines. Partitions of integers as states of these stochastic dynamic programming problems involves combinatorial aspects of SDDP problems. Under the assumption of identical "basic costs" (in other words of "unit distances") and independent and identically distributed requirements we will show (in many cases) by means of combinatorial ideas that decisions for feasible states with least square sums of their parts are optimal solutions. Corresponding Markov kernels are called Partitions-Requirements-Matrices (PRMs). Optimal decisions of such problems can be used as approximate solutions of corresponding SDDP problems, in which the basic costs differ only slightly from each other or as starting decisions if corresponding SDDP problems are solved by iterative methods, such as the Howard algorithm.



Hotz, Thomas;
Extrinsic vs intrinsic means on the circle. - In: Geometric science of information : first international conference, GSI 2013, Paris, France, August 28 - 30, 2013 ; proceedings. - Berlin [u.a.] : Springer, ISBN 978-3-642-40020-9, (2013), S. 433-440

http://dx.doi.org/10.1007/978-3-642-40020-9_47
Fleischner, Herbert; Stiebitz, Michael
Some remarks on the cycle plus triangles problem. - In: New York [u.a.] : Springer, ISBN 978-1-4614-7253-7, (2013), S. 119-125

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, 2013 - 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.



http://www.db-thueringen.de/servlets/DocumentServlet?id=22747
Trunk, Carsten;
Locally definitizable operators: the local structure of the spectrum - Ilmenau : Techn. Univ., Inst. für Mathematik, 2013 - 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.



http://www.db-thueringen.de/servlets/DocumentServlet?id=22710
Anderson, Brian D. O.; Ilchmann, Achim; Wirth, Fabian R.
Stabilizability of linear time-varying systems. - In: Systems & control letters - Amsterdam [u.a.] : Elsevier, ISSN 1872-7956, 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 1432-1807, 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, 2013 - 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.



http://www.db-thueringen.de/servlets/DocumentServlet?id=22652
Klöppel, Michaell; Gabash, Aouss; Geletu, Abebe; Li, Pu
Chance constrained optimal power flow with non-Gaussian distributed uncertain wind power generation. - In: 2013 12th International Conference on Environment and Electrical Engineering (EEEIC) : 5 - 8 May 2013, Wroclaw, Poland. - Piscataway, NJ : IEEE, ISBN 978-1-4673-3060-2, (2013), S. 265-270

http://dx.doi.org/10.1109/EEEIC.2013.6549628