Stabilizability of linear switching systems

A complete characterization of stabilizability for linear switching systems is not available in the literature. In this paper, we show that the asymptotic stabilizability of linear switching systems is equivalent to the existence of a hybrid Lyapunov function for the controlled system, for a suitabl...

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Published inNonlinear analysis. Hybrid systems Vol. 2; no. 3; pp. 750 - 764
Main Authors De Santis, E., Di Benedetto, M.D., Pola, G.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.08.2008
Subjects
Hybrid systems
Kalman decomposition
Linear switching systems
Lyapunov functions
Stabilizability
Stabilizability
Hybrid systems
Lyapunov functions
Kalman decomposition
Linear switching systems
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Summary:A complete characterization of stabilizability for linear switching systems is not available in the literature. In this paper, we show that the asymptotic stabilizability of linear switching systems is equivalent to the existence of a hybrid Lyapunov function for the controlled system, for a suitable control strategy. Further, we prove that asymptotic stabilizability of a switching system with minimum dwell time, is equivalent to Input to State Stability (ISS) of the controlled switching system, with a stabilizing control law. We then derive some structural reductions of the hybrid state space, which allow a decomposition of the original problem into simpler subproblems. The relationships between this approach and the well-known Kalman decomposition of linear dynamic control systems are explored.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:1751-570X
DOI:10.1016/j.nahs.2007.11.007