MURAL - Maynooth University Research Archive Library

    Convex Cones, Lyapunov Functions, and the Stability of Switched Linear Systems

    Shorten, Robert N. and Mason, Oliver and Wulff, Kai (2005) Convex Cones, Lyapunov Functions, and the Stability of Switched Linear Systems. In: Switching and Learning in Feedback Systems : European Summer School on Multi-Agent Control, Maynooth, Ireland, September 8-10, 2003, Revised Lectures and Selected Papers. Lecture Notes in Computer Science (3355). Springer-Verlag, Berlin Heidelberg, pp. 31-46. ISBN 9783540244578

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    Recent research on switched and hybrid systems has resulted in a renewed interest in determining conditions for the existence of a common quadratic Lyapunov function for a finite number of stable LTI systems. While efficient numerical solutions to this problem have existed for some time, compact analytical conditions for determining whether or not such a function exists for a finite number of systems have yet to be obtained. In this paper we present a geometric approach to this problem. By making a simplifying assumption we obtain a compact time-domain condition for the existence of such a function for a pair of LTI systems. We show a number of new and classical Lyapunov results can be obtained using our framework. In particular, we demonstrate that our results can be used to obtain compact time-domain versions of the SISO Kalman- Yacubovich-Popov lemma, the Circle Criterion, and stability multiplier criteria. Finally, we conclude by posing a number of open questions that arise as a result of our approach.

    Item Type: Book Section
    Additional Information: The published version of this article is available at DOI: 10.1007/978-3-540-30560-6_2
    Keywords: Convex Cones; Lyapunov Functions; Stability; Switched Linear Systems;
    Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
    Faculty of Science and Engineering > Mathematics and Statistics
    Item ID: 6235
    Identification Number:
    Depositing User: Oliver Mason
    Date Deposited: 07 Jul 2015 15:43
    Publisher: Springer-Verlag
    Refereed: Yes
      Use Licence: This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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