Multiple lyapunov functions approach to observer - based H control for switched systems

Abstract

This article investigates the issue of H control for a class of continuous-time switched Lipschitz nonlinear systems. None of the individual subsystems is assumed to be stabilisable with H disturbance attenuation. Based on a generalised multiple Lyapunov functions (GMLFs) approach, which removes the nonincreasing requirement at switching points, a sufficient condition for the solvability of the H control problem under a state estimation-dependent switching law is presented. Observers, controllers and a switching law are simultaneously designed. As an extension, a sufficient condition for exponential stabilisability is also given.