Guaranteed Cost Control for Uncertain Discrete-time Switched Systems

Abstract

Guaranteed cost control for a class of linear discrete-time switched systems with parameter uncertainty is studied. The purpose is to design a state feedback control law such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Two different sufficient conditions on the existence of guaranteed cost controllers are derived based on a switched Lyapunov function (SLF) method together with linear matrix inequality (LMI) approach. Furthermore, a convex optimization problem with LMIs constraints is formulated to design a suboptimal guaranteed cost controller. A numerical example demonstrates the effect of the proposed design approach.