Feedback Stabilization and Lyapunov Functions F H Clarke
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Feedback Stabilization and Lyapunov Functions F. H. Clarke Institut Girard Desargues (Bat 101) Universite Claude Bernard Lyon I (La Doua) 69622 Villeurbanne France Yu. S. Ledyaev Steklov Institute of Mathematics Moscow 117966, Russia L. Rifford Institut Girard Desargues (Bat 101) Universite Claude Bernard Lyon I (La Doua) 69622 Villeurbanne France R. J. Stern Department of Mathematics and Statistics Concordia University Montreal, Quebec H4B 1R6, Canada December 17, 1998 Abstract Given a locally defined, nondifferentiable but Lipschitz Lyapunov func- tion, we construct a (discontinuous) feedback law which stabilizes the underlying system to any given tolerance. A further result shows that suitable Lyapunov functions of this type exist under mild assumptions. We also establish a robustness property of the feedback relative to mea- surement error commensurate with the sampling rate of the control im- plementation scheme. 0Key words:Asymptotic stabilizability, discontinuous feedback law, system sampling, lo- cally Lipschitz Lyapunov function, nonsmooth analysis, robustness 0Mathematical Subject Classification: 93D05, 93D20, 34D20, 26B05 1
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- feedback law
- cally lipschitz
- yet fails
- any globally
- lyapunov function
- system
- lipschitz lyapunov
