Guaranteed cost control for uncertain discrete-time switched systems with time-delay

This paper deals with the guaranteed cost control problem for a class of uncertain linear discrete-time switched systems with time-delay under arbitrary switching laws. 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. A sufficient condition on the existence of guaranteed cost controllers is derived based on Lyapunov theory together with linear matrix inequality (LMI) approach. Furthermore, a convex optimization problem with LMIs constraints is formulated to select the suboptimal guaranteed cost controller. A numerical example demonstrates the validity of the proposed design approach.