Finite-Time l1-Gain Control for Positive Switched Systems with Time-Varying Delay via Delta Operator Approach

Abstract

This paper is concerned with the problem of finite-time $l_1$-gain control for positive switched systems with time-varying delay via delta operator approach. Firstly, sufficient conditions which can guarantee the $l_1$-gain finite-time boundedness of the underlying system are given by using the average dwell time approach and constructing an appropriate copositive type Lyapunov-Krasovskii functional in delta domain. Moreover, the obtained conditions can unify some previously suggested relevant results seen in literature of both continuous and discrete systems into the delta operator framework. Then, based on the results obtained, a state feedback controller is designed to ensure that the resulting closed-loop system is finite-time bounded with an $l_1$-gain performance. Finally, a numerical example is presented to demonstrate the effectiveness and feasibility of the proposed method.