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Prof. Dr. Achim Ilchmann

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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
Huang, Junjie; Sun, Junfeng; Chen, Alatancang; Trunk, Carsten
The invertibility of 2 x 2 operator matrices. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2014. - 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.
Jacob, Birgit; Langer, Matthias; Trunk, Carsten
Variational principles for self-adjoint operator functions arising from second-order systems. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2014. - Online-Ressource (PDF-Datei: 30 S., 455 KB). . - (Preprint. - M14,09)
Boccia, Andrea; , ; ,
Stability and feasibility of state constrained MPC without stabilizing terminal constraints. - In: Systems & control letters. - Amsterdam [u.a.] : Elsevier, ISSN 1872-7956, Bd. 72 (2014), S. 14-21
Ilchmann, Achim; Reis, Timo
Outer transfer functions of differential-algebraic systems. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2014. - 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.
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 1090-2732, Bd. 257 (2014), 8, S. 2984-3047
Snoo, Henk; deFleige, Andreas; Hassi, Seppo; Winkler, Henrik;
Non-semi-bounded closed symmetric forms associated with a generalized Friedrichs extension. - In: Proceedings. Mathematics / The Royal Society of Edinburgh. - Cambridge [u.a.] : Cambridge Univ. Press, 1943- ; ZDB-ID: 2036780-6, ISSN 1473-7124, Bd. 144 (2014), 4, S. 731-745
Reis, Timo; Selig, Tilman
Zero dynamics and root locus for a boundary controlled heat equation. - Hamburg : Fachbereich Mathematik, Univ. Hamburg, 2014. - Online-Ressource (PDF-Datei: 29 S., 229 KB). . - (Hamburger Beiträge zur Angewandten Mathematik. - 2014,08)
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 1095-7138, Bd. 52 (2014), 3, S. 1935-1957
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 1095-7138, Bd. 52 (2014), 1, S. 581-605