Symmetry in de Branges almost Pontryagin spaces. - In: Integral equations and operator theory, ISSN 1420-8989, Bd. 76 (2013), 2, S. 179-212
http://dx.doi.org/10.1007/s00020-013-2051-7
Zero dynamics and stabilization for linear DAEs. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2013. - Online-Ressource (PDF-Datei: 19 S., 140 KB). - (Preprint ; M13,08)
We study linear differential-algebraic multi-input multi-output systems which are not necessarily regular and investigate the asymptotic stability of the zero dynamics and stabilizability. To this end, the concepts of autonomous zero dynamics, transmission zeros, right-invertibility, stabilizability in the behavioral sense and detectability in the behavioral sense are introduced and algebraic characterizations are derived. It is then proved, for the class of right-invertible systems with autonomous zero dynamics, that asymptotic stability of the zero dynamics is equivalent to three conditions: stabilizability in the behavioral sense, detectability in the behavioral sense, and the condition that all transmission zeros of the system are in the open left complex half-plane. Furthermore, for the same class, it is shown that we can achieve, by a compatible control in the behavioral sense, that the Lyapunov exponent of the interconnected system equals the Lyapunov exponent of the zero dynamics.
http://www.db-thueringen.de/servlets/DocumentServlet?id=22328
Controllability of linear differential-algebraic systems - a survey. - In: Surveys in differential-algebraic equations, (2013), S. 1-61
Advances and applications of chance-constrained approaches to systems optimisation under uncertainty. - In: International journal of systems science, ISSN 1464-5319, Bd. 44 (2013), 7, S. 1209-1232
http://dx.doi.org/10.1080/00207721.2012.670310
Axioms for infinite matroids. - In: Advances in mathematics, ISSN 1090-2082, Bd. 239 (2013), S. 18-46
https://doi.org/10.1016/j.aim.2013.01.011
Prescribed edges and forbidden edges for a cycle in a planar graph. - In: Discrete applied mathematics, ISSN 1872-6771, Bd. 161 (2013), 12, S. 1734-1738
https://doi.org/10.1016/j.dam.2011.08.020
Zero dynamics and funnel control for linear electrical circuits. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2013. - Online-Ressource (PDF-Datei: 25 S., 217,2 KB). - (Preprint ; M13,07)
We consider electrical circuits containing linear resistances, capacitances, inductances. The circuits can be described by differential-algebraic input-output systems, where the input consists of voltages of voltage sources and currents of current sources and the output consists of currents of voltage sources and voltages of current sources. We generalize a characterization of asymptotic stability of the circuit and give sufficient topological criteria for its invariant zeros being located in the open left half-plane. We show that asymptotic stability of the zero dynamics can be characterized by means of the interconnectivity of the circuit and that it implies that the circuit is high-gain stabilizable with any positive high-gain factor. Thereafter we consider the output regulation problem for electrical circuits by funnel control. We show that for circuits with asymptotically stable zero dynamics, the funnel controller achieves tracking of a class of reference signals within a pre-specified funnel; this means in particular that the transient behaviour of the output error can be prescribed and the funnel controller does neither incorporate any internal model for the reference signals nor any identification mechanism, it is simple in its design. The results are illustrated by a simulation of a discretized transmission line.
http://www.db-thueringen.de/servlets/DocumentServlet?id=22165
Linear fractional transformations of Nevanlinna functions associated with a nonnegative operator. - In: Complex analysis and operator theory, ISSN 1661-8262, Bd. 7 (2013), 2, S. 331-362
https://doi.org/10.1007/s11785-011-0197-3
Properly optimal elements in vector optimization with variable ordering structures. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2013. - Online-Ressource (PDF-Datei: 27 S., 311,4 KB). - (Preprint ; M13,05)
In this paper, proper optimality concepts in vector optimization with variable ordering structures are introduced for the first time and characterization results via scalarizations are given. New type of scalarizing functionals are presented and their properties are discussed. The scalarization approach suggested in the paper does not require convexity and boundedness conditions.
http://www.db-thueringen.de/servlets/DocumentServlet?id=22044
Symmetry in de Branges almost Pontryagin spaces. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2013. - Online-Ressource (PDF-Datei: 33 S., 303,1 KB). - (Preprint ; M13,06)
In many examples of de Branges spaces symmetry appears naturally. Presence of symmetry gives rise to a decomposition of the space into two parts, the "even" and the "odd" part, which themselves can be regarded as de Branges spaces. The converse question is to decide whether a given space is the "even" part or the "odd" part of some symmetric space, and, if yes, to describe the totality of all such symmetric spaces. We consider this question in an indefinite (almost Pontryagin space) setting, and give a complete answer. Interestingly, it turns out that the answers for the "even" and "odd" cases read quite differently; the latter is significantly more complex.
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