Geoffrey Eisenbarth, John M. Davis, Ian Gravagne
Abstract:
In this paper, we extend the results of [8, 15, 22],
which provide sufficient conditions for the global exponential stability
of switched systems under arbitrary switching via the existence of a
common quadratic Lyapunov function. In particular, we extend the Lie
algebraic results in [15] to switched systems with hybrid
non-uniform discrete and continuous domains, a direct unifying
generalization of switched systems on R and Z,
and extend the results in [8, 22] to a larger class
of switched systems, namely those whose subsystem matrices are
simultaneously triangularizable. In addition, we explore
an easily checkable characterization of our required hypotheses
for the theorems. Finally, conditions are provided under which
there exists a stabilizing switching pattern for a collection of
(not necessarily stable) linear systems that are simultaneously
triangularizable and separate criteria are formed which imply
the stability of the system under a given switching pattern
given a priori.
Submitted September 13, 2013. Published March 5, 2014.
Math Subject Classifications: 93C30, 93D05, 93D30.
Key Words: Switched system; common quadratic Lyapunov function;
simultaneously triangularizable; hybrid system; time scales.
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Geoffrey Eisenbarth Department of Mathematics Baylor University Waco, TX 76798, USA email: Geoffrey_Eisenbarth@baylor.edu |
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John M. Davis Department of Mathematics Baylor University Waco, TX 76798, USA email: John_M_Davis@baylor.edu |
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Ian Gravagne Department of Electrical and Computer Engineering Baylor University Waco, TX 76798, USA email: Ian_Gravagne@baylor.edu |
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