ROBUST STABILITY ANALYSIS AND CONTROL DESIGN FOR SWITCHED UNCERTAIN POLYTOPIC SYSTEMS

This paper is dedicated to the study of robust stability analysis and control synthesis for discrete time uncertain switching systems under arbitrary switching. Polytopic uncertainties are considered. We show that Lyapunov functions that depend on the uncertain parameter and that take into account the structure of the system may be used in order to reduce the conservatism related to uncertainty problems. New LMI condition are obtained. We introduce the switched parameter dependent Lyapunov functions, i.e. functions that are based on a structure similar to that of the uncertain switched system. Necessary and sufficient LMI conditions for the existence of these functions are presented. A numerical example illustrates the conservatism of existing results. The approach is extended to switched state feedback design or state reconstruction for uncertain switched systems.