Feedback stabilization and Lyapunov functions

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, robustnes