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.

Keywords:

• switched systems
• observer
• H _∞ control
• exponential stabilisation
• multiple Lyapunov functions

Acknowledgements

This work was supported by the NSFC under Grants 61174073 and 60874024.