Results on input-to-state stability for hybrid systems

We show that, like continuous-time systems, zero-input locally asymptotically stable hybrid systems are locally input-to-state-stable (LISS). We demonstrate by examples that, unlike continuous-time systems, zero-input locally exponentially stable hybrid systems may not be LISS with linear gain, inpu...

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Bibliographic Details
Published inProceedings of the 44th IEEE Conference on Decision and Control pp. 5403 - 5408
Main Authors Chaohong Cai, Teel, A.R.
Format Conference Proceeding
LanguageEnglish
Published IEEE 2005
Subjects
Asymptotic stability
Chaos
Difference equations
Differential equations
Gain
Lyapunov method
Noise robustness
Nonlinear control systems
Robust control
Robust stability
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ISBN9780780395671
0780395670
ISSN0191-2216
DOI10.1109/CDC.2005.1583021

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Summary:We show that, like continuous-time systems, zero-input locally asymptotically stable hybrid systems are locally input-to-state-stable (LISS). We demonstrate by examples that, unlike continuous-time systems, zero-input locally exponentially stable hybrid systems may not be LISS with linear gain, input-to-state stable (ISS) hybrid systems may not admit any ISS Lyapunov function, and nonuniform ISS hybrid systems may not be (uniformly) ISS. We then provide a strengthened ISS condition as an equivalence to the existence of an ISS Lyapunov function for hybrid systems. This strengthened condition reduces to standard ISS for continuous-time and discrete-time systems. Finally under some other assumptions we establish the equivalence among ISS, several asymptotic characterizations of ISS, and the existence of an ISS Lyapunov function for hybrid systems.
ISBN:9780780395671
0780395670
ISSN:0191-2216
DOI:10.1109/CDC.2005.1583021