Stability of Discrete-Time Switched Systems With Multiple Equilibria Using a Common Quadratic Lyapunov Function

Abstract

This letter studies stability of a class of discrete-time switched systems under arbitrary switching in which each subsystem has a different equilibrium. We extend the concept of a common quadratic Lyapunov function in order to characterize asymptotic stability of a set that contains all the equilibria. The results are applied to a model of visuomotor adaptation to analyze boundedness of solutions when the visual error measurement is intermittent.