On Control-Lyapunov Functions for Hybrid Time-Varying Systems

We explicitly construct strict input-to-state stable Lyapunov functions for time varying hybrid systems, in terms of given nonstrict Lyapunov functions and persistency of excitation parameters. This provides a hybrid analog of our earlier continuous time Lyapunov function constructions. Our results...

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Bibliographic Details
Published inProceedings of the 45th IEEE Conference on Decision and Control pp. 3265 - 3270
Main Authors Malisoff, M., Mazenc, F.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.12.2006
IEEE Press
SeriesCDC 06
Subjects
Computer Science
Control systems
Design engineering
discrete time and hybrid time-varying systems
Discrete time systems
Feedback
input-to-state stability
Lyapunov method
Mathematics
Nonlinear dynamical systems
Robustness
Stability
Strict Lyapunov functions
Time varying systems
USA Councils
SYSTEME HYBRIDE
FONCTION LYAPUNOV STRICTE
INPUT-TO-STATE STABILITY
TEMPS DISCRET
DISCRETE TIME AND HYBRID TIME-VARYING SYSTEMS
THEOREM DE MATROSOV
STABILITE
AUTOMATIQUE
STRICT LYAPUNOV FUNCTIONS
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ISBN9781424401710
1424401712
ISSN0191-2216
DOI10.1109/CDC.2006.377293

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Summary:We explicitly construct strict input-to-state stable Lyapunov functions for time varying hybrid systems, in terms of given nonstrict Lyapunov functions and persistency of excitation parameters. This provides a hybrid analog of our earlier continuous time Lyapunov function constructions. Our results are new even for the special case of discrete time systems since our formulas involve finite sums of persistency of excitation parameters. We also construct explicit strict Lyapunov functions for systems satisfying appropriate nonstrict hybrid analogs of the conditions from Matrosov's theorem
ISBN:9781424401710
1424401712
ISSN:0191-2216
DOI:10.1109/CDC.2006.377293