Feedback Stabilization and Lyapunov Functions

Given a locally defined, nondifferentiable but Lipschitz Lyapunov function, 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 measurement error commensurate with the sampling rate of the control implementation scheme. 0Key words:Asymptotic stabilizability, discontinuous feedback law, system sampling, locally Lipschitz Lyapunov function, nonsmooth analysis, robustness 0Mathematical Subject Classification: 93D05, 93D20, 34D20, 26B05 1 

• Type: Journal
• Year: 2000
• Where: SIAMCO
• Authors: F. H. Clarke, Yu. S. Ledyaev, L. Rifford, R. J. Stern
• Keywords: Feedback Law, Lipschitz Lyapunov Function, Lyapunov Function, SIAMCO 2000