On the Existence of Control Lyapunov Functions and State-Feedback Laws for Hybrid Systems

For a class of hybrid systems given in terms of constrained differential and difference equations/inclusions, we study the existence of control Lyapunov functions when compact sets are asymptotically stable as well as the stabilizability properties guaranteed when control Lyapunov functions exist. A...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2013-12, Vol.58 (12), p.3242-3248
Main Author: Sanfelice, Ricardo G.
Format: Article
Language:English
Subjects:
Aerospace electronics
Asymptotic stability
Control systems
hybrid control
hybrid systems
Lyapunov methods
Nonlinear systems
Robustness
selections
set-valued analysis
Time-domain analysis
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Summary:For a class of hybrid systems given in terms of constrained differential and difference equations/inclusions, we study the existence of control Lyapunov functions when compact sets are asymptotically stable as well as the stabilizability properties guaranteed when control Lyapunov functions exist. An existence result asserting that asymptotic stabilizability of a compact set implies the existence of a smooth control Lyapunov function is established. When control Lyapunov functions are available, conditions guaranteeing the existence of stabilizing continuous state-feedback control laws are provided.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2013.2264851