Feedback Stabilization and Lyapunov Functions

Authors:
F. H. Clarke;Yu. S. Ledyaev;L. Rifford;R. J. Stern
Affiliations:
-;-;-;-
Venue:
SIAM Journal on Control and Optimization
Year:
2000

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Abstract

Given a locally defined, nondifferentiable but Lipschitz Lyapunov function, we employ it in order to construct a (discontinuous) feedback law which stabilizes the underlying system to any given tolerance. A converse result shows that suitable Lyapunov functions of this type exist under mild assumptions. We also establish that the feedback in question possesses a robustness property relative to measurement error, despite the fact that it may not be continuous.