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Prof. Dr. Achim Ilchmann

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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 1095-7162, 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 1095-7138, 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 2196-677X, 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 1617-7061, 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 1617-7061, 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, 2013. - 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, 2013. - 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, 2013. - Online-Ressource (PDF-Datei: 19 S., 411 KB). . - (Preprint. - M13,15)
http://www.db-thueringen.de/servlets/DocumentServlet?id=23174
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
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.



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