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

This paper deals with the design of guaranteed cost observers for a class of discrete-time switched systems with time-delay under arbitrary switching law. The objective is to design a linear memoryless observer such that for all admissible uncertainties, the resulting augmented system is asymptotically stable and satisfies the proposed guaranteed cost performance. A sufficient condition on the existence of guaranteed cost observers is derived by means of a Lyapunov function method together with linear matrix inequality (LMI) approach, and the guaranteed cost observers can be obtained. Furthermore, a convex optimization problem is formulated to design the suboptimal guaranteed cost observer. A numerical example demonstrates the effect of the proposed design approach.