Multiple Lyapunov functions approach to observer-basedH∞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. Keywords: switched systemsobserver H ∞ controlexponential stabilisationmultiple Lyapunov functions Acknowledgements This work was supported by the NSFC under Grants 61174073 and 60874024.