Stability and L1L1-gain controller design for positive switched systems with mixed time-varying delays

This paper investigates the problems of stability and L1L1-gain controller design for positive switched systems with mixed time-varying delays. The mixed time-varying delays are presented in the forms of discrete delay and distributed delay. The purpose of this paper is to design a class of switching signals and a state feedback controller for the considered system such that the resulting closed-loop system is exponentially stable with L1L1-gain performance. By constructing an appropriate co-positive type Lyapunov–Krasovskii functional and using the average dwell time approach, we propose a sufficient condition to ensure the exponential stability with weighted L1L1-gain performance for the system. On the basis of the obtained results, an effective method for designing such controller is established. Finally, a numerical example is presented to demonstrate the feasibility of the results obtained.