Abstract:
We show that (pre-)asymptotic stability, which is a natural generalization of asymptotic stability, of a compact set for a hybrid system satisfying mild regularity assump...Show MoreMetadata
Abstract:
We show that (pre-)asymptotic stability, which is a natural generalization of asymptotic stability, of a compact set for a hybrid system satisfying mild regularity assumptions is equivalent to the existence of a smooth Lyapunov function. In this new converse Lyapunov theorem for (pre-)asymptotic stability, we no longer require the assumption that the basin of attraction is open (cf. [1, Theorem 1]). Furthermore, we demonstrate several applications of the converse Lyapunov theorem by establishing robustness of pre-asymptotic stability to various types of perturbations and achieving input-to-state stabilization for hybrid-feedback-control systems.
Published in: 2007 American Control Conference
Date of Conference: 09-13 July 2007
Date Added to IEEE Xplore: 30 July 2007
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