A Lyapunov-Like Characterization of Robustness of Pointwise Asymptotic Stability for Differential Inclusions

Rafal Goebel1

  • 1Loyola University Chicago

Details

15:10 - 15:30 | Wed 4 Sep | Room FH 4 | WeD4.3

Session: Set-Valued and Nonsmooth Analysis in Systems and Control: Generalized Lyapunov Methods and Beyond I

Abstract

Given a dynamical system, pointwise asymptotic stability (a.k.a. semistability) of a set requires that every point in the set be a Lyapunov stable equilibrium, and that every solution converge to one of the equilibria in the set. This note shows that robustness of this property, for a compact set in a setting of a differential inclusion subject to standard basic assumptions, can be equivalently characterized by the existence of a continuous set-valued Lyapunov function.