Stability and stabilization of positive switched systems under asynchronous switching

This paper investigates stability and stabilization of positive switched systems under asynchronous switching, which means that the switching of the controller has a delay to that of the system mode. First, two sufficient conditions for the stability of autonomous systems are established. The first one is obtained by using the linear copositive Lyapunov function incorporated with linear programming method, which allows the Lyapunov function to increase during the running time of the active mode. The second one is only based on linear programming. Then, by combining two obtained results, the state-feedback stabilization of non-autonomous systems under asynchronous switching is solved and an average dwell time is designed. Finally, an example is given to illustrate the effectiveness of the obtained results.