A New Switching Strategy for Exponential Stabilization of Uncertain Discrete-Time Switched Linear Systems in Guaranteed Cost Control Problem

Uncertain switched linear systems are known as an important class of control systems. Performance of these systems is affected by uncertainties and their stabilization is a main concern of recent studies. Existing work on stabilization of these systems only provides asymptotical stabilization via designing switching strategy and state-feedback controller. In this paper, considering a given infinite-horizon cost function, a new switching strategy and a state-feedback control laws are designed to exponentially stabilize Uncertain Discrete-Time Switched Linear Systems (UDSLS). Our design procedure consists of two steps. First, we generalize the exponential stabilization theorem of nonlinear systems into UDSLS. Second, a new stabilizing switching strategy based on the Common Lyapunov Function technique presented. Hence, a sufficient condition on the existence of statefeedback controller is provided in the form of Linear Matrix Inequality. Besides, convergence rate of the states is obtained and the upper bound of the cost is calculated. Finally, effectiveness of the proposed method is verified via numerical example.