Publications

Berger, Thomas; Ilchmann, Achim;
On stability of time-varying linear differential-algebraic equations. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2010. - Online-Ressource (PDF-Datei: 25 S., 284,9 KB). - (Preprint ; M10,12)

We develop a stability theory for time-varying linear differential algebraic equations (DAEs). Standard stability concepts for ODEs are formulated for DAEs and characterized. Lyapunovs direct method is derived as well as the converse of the stability theorems. Stronger results are achieved for DAEs which are transferable into standard canonical form; in this case the existence of the generalized transition matrix is exploited.

http://www.db-thueringen.de/servlets/DocumentServlet?id=16643

Brandstädt, Andreas; Le, Van Bang; Rautenbach, Dieter
Exact leaf powers. - In: Theoretical computer science, Bd. 411 (2010), 31/33, S. 2968-2977

http://dx.doi.org/10.1016/j.tcs.2010.04.027

Hackl, Christoph; Hopfe, Norman; Ilchmann, Achim; Mueller, Markus; Trenn, Stephan
Funnel control for systems with relative degree two. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2010. - Online-Ressource (PDF-Datei: 36 S., 523,7 KB). - (Preprint ; M10,06)

Tracking of reference signals yref(&hahog;) by the output y(&hahog;) of linear (as well as a considerably large class of nonlinear) single-input, single-output system is considered. The system is assumed to have strict relative degree two with ("weak") stable zero dynamics. The control objective is tracking of the error e = y - yref and its derivative e&hahog; within two prespecified performance funnels, resp. This is achieved by the so called 'funnel controller': u(t) = -k0(t)2e(t) - k1(t)e&hahog;(t), where the simple proportional error feedback has gain functions k0 and k1 designed in such a way to preclude contactof e and e&hahog; with the funnel boundaries, resp. The funnel controller also ensures boundedness of all signals. --- We also show that the same funnel controller is (i) applicable to relative degree one systems, (ii) allows for input constraints provided a feasibility condition (formulated in terms of the system data, the saturation bounds, the funnel data, bounds on the reference signal and the initial state) holds, (iii) is robust in terms of the gap metric: if a system is sufficiently close to a system with relative degree two, stable zero dynamics and positive high-frequency gain, but does not necessarily have these properties, then for small initial values the funnel controller also achieves the control objective. Finally, we illustrate the theoretical results by experimental results: the funnel controller is applied to a rotatory mechanical system for position control.

http://www.db-thueringen.de/servlets/DocumentServlet?id=16114

Azizov, Tomas Ya.; Trunk, Carsten
On domains of PT symmetric operators related to -y"(x) + (-1) n x 2n y(x). - In: Journal of physics. Mathematical and theoretical. - Bristol : IOP Publ., 2007- , ISSN: 1751-8121 , ZDB-ID: 1363010-6, ISSN 1751-8121, Bd. 43.2010, 17, 175303, insges. 13 S.

http://dx.doi.org/10.1088/1751-8113/43/17/175303

Harant, Jochen; Rautenbach, Dieter; Recht, Peter; Regen, Friedrich
Packing edge-disjoint cycles in graphs and the cyclomatic number. - In: Discrete mathematics, Bd. 310 (2010), 9, S. 1456-1462

http://dx.doi.org/10.1016/j.disc.2009.07.017