Robust stabilization of discrete switched systems with time delay

This paper investigates robust stabilization of discrete switched systems with time delay. Based on multiple Lyapunov functions technique, we develop state feedback controllers to stabilize the switched systems. The sufficient conditions for the existence of controller are presented using a set of matrix inequalities, which can be solved by a technique called itinerant linear matrix inequality algorithm (ILMI), and the controller gains are also obtained simultaneously. Finally, a numerical example is provided to demonstrate the application of the proposed method.