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    Some results on the stability of positive switched linear systems


    Mason, Oliver and Shorten, Robert N. (2004) Some results on the stability of positive switched linear systems. In: 43rd IEEE Conference on Decision and Control, 2004 (CDC). IEEE, pp. 4601-4606. ISBN 0780386825

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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: Book Section
    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;
    Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
    Item ID: 2221
    Identification Number: https://doi.org/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
    Funders: Science Foundation Ireland grant 00/PI.1/C067, Science Foundation Ireland Basic Research Grant 04/BR/m0061, Enterprise Ireland grant SC/2000/084/Y
    URI:

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