Stability and -Gain Control of Positive Switched Systems with Time-Varying Delays via Delta Operator Approach

This paper investigates the problems of stability and -gain controller design for positive switched systems with time-varying delays via delta operator approach. The purpose is to design a switching signal and a state feedback controller such that the resulting closed-loop system is exponentially stable with -gain performance. Based on the average dwell time approach, a sufficient condition for the existence of an -gain controller for the considered system is established by constructing an appropriate copositive type Lyapunov-Krasovskii functional in delta domain. Moreover, the obtained conditions can unify some previously suggested relevant methods in the literature of both continuous- and discrete-time systems into the delta operator framework. Finally, a numerical example is presented to explicitly demonstrate the effectiveness and feasibility of the proposed method.