Mason, Oliver and Shorten, Robert
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.
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.
||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 ©  IEEE. Reprinted from 43rd IEEE Conference on Decision and Control, 2004.
||Lyapunov methods; asymptotic stability; linear systems; multidimensional systems; stability criteria; time-varying systems;
||Science & Engineering > Hamilton Institute
||27 Oct 2010 15:58
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||Decision and Control, 2004. CDC. 43rd IEEE Conference on , ISBN 0-7803-8682-5
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