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Some results on the stability of positive switched linear systems

Mason, Oliver and Shorten, Robert (2004) Some results on the stability of positive switched linear systems. Decision and Control, 2004. CDC. 43rd IEEE Conference on , ISBN 0-7803-8682-5 , 5. pp. 4601-4606.

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Abstract

In this paper, we present a number of results concerned with the stability of positive switched linear systems. In particular, we show that a recent conjecture concerning the existence of common quadratic Lyapunov functions (CQLFs) for positive LTI systems is true for second order systems, and establish a class of switched linear systems for which CQLF existence is equivalent to exponential stability under arbitrary switching. However, this conjecture is false for higher dimensional systems and we illustrate this fact with a counterexample. A number of stability criteria for positive switched linear systems based on common diagonal Lyapunov functions (CDLFs) are also presented, as well as a necessary and sufficient condition for a general pair of positive LTI systems to have a CDLF. To the best of the authors’ knowledge, this is the first time that a necessary and sufficient condition for CDLF existence for n-dimensional systems has appeared in the literature.

Item Type: Article
Additional Information: This work was partially supported by Science Foundation Ireland grant 00/PI.1/C067, Science Foundation Ireland Basic Research Grant 04/BR/m0061 and Enterprise Ireland grant SC/2000/084/Y. Neither Science Foundation Ireland nor Enterprise Ireland is responsible for any use of data appearing in this publication. Copyright © [2004] IEEE.   Reprinted from 43rd IEEE Conference on Decision and Control, 2004.
Keywords: Lyapunov methods; asymptotic stability; linear systems; multidimensional systems; stability criteria; time-varying systems;
Subjects: Science & Engineering > Hamilton Institute
Item ID: 2221
Identification Number: DOI: 10.1109/CDC.2004.1429509
Depositing User: Oliver Mason
Date Deposited: 27 Oct 2010 15:58
Journal or Publication Title: Decision and Control, 2004. CDC. 43rd IEEE Conference on , ISBN 0-7803-8682-5
Publisher: IEEE
Refereed: Yes
URI:

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