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Prof. Dr. Achim Ilchmann

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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 1095-7138, Bd. 54 (2016), 3, S. 1504-1534
Behrndt, Jussi; Möws, Roland; Trunk, Carsten;
Eigenvalue estimates for operators with finitely many negative squares. - Ilmenau : Technische Universität, Institut für Mathematik, 2016. - 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.
Worthmann, Karl; Braun, Philipp; Proch, Michael; Schlüchtermann, Jörg; Pannek, Jürgen;
On contractual periods in supplier development. - In: IFAC-PapersOnLine. - Frankfurt : Elsevier, ISSN 2405-8963, Bd. 49 (2016), 2, S. 60-65
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, ISSN 1096-0813, Bd. 439 (2016), 2, S. 864-895
Gernandt, Hannes; Trunk, Carsten;
Eigenvalue placement for regular matrix pencils with rank one perturbations. - Ilmenau : Technische Universität, Institut für Mathematik, 2016. - 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.
Knobloch, Jürgen; Vielitz, Martin
Non-conservative perturbations of homoclinic snaking scenarios. - In: Journal of differential equations. - Orlando, Fla. : Elsevier, ISSN 1090-2732, Bd. 260 (2016), 1, S. 517-566
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
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
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, ISBN 978-1-4799-7886-1, (2015), S. 5593-5598
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 2405-8963, Bd. 48 (2015), 23, S. 129-135