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

Preview

Download (264kB) | Preview

Abstract

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:	https://doi.org/10.1007/978-3-540-30560-6_2
Depositing User:	Oliver Mason
Date Deposited:	07 Jul 2015 15:43
Publisher:	Springer-Verlag
Refereed:	Yes
URI:
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

Repository Staff Only(login required)

Item control page

Downloads

Origin of downloads