Guaranteed cost control of uncertain discrete-time switched linear systems with actuator saturation

The problem of guaranteed cost control is investigated for a class of uncertain discrete-time switched linear systems subject to actuator saturation. The purpose is to design a state feedback control law such that the closed-loop system is asymptotically stable and the upper-bound of the cost function is minimized. Based on the switched Lyapunov function approach, some sufficient conditions for the existence of guaranteed cost controllers are obtained. Furthermore, a convex optimization problem with linear matrix inequalities (LMI) constraints is formulated to determine the minimum upper-bound of the cost function. Finally, a numerical example is given to demonstrate the effectiveness of the proposed design method.