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 its 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, a new switching strategy and a state-feedback control law are designed to exponentially stabilize Uncertain Discrete-Time Switched Linear Systems (UDSLS), considering a given infinite-horizon cost function. Our design procedure consists of three steps. First, we generalize the exponential stabilization theorem of nonlinear systems to UDSLS. Second, based on the Common Lyapunov Function technique, a new stabilizing switching strategy is presented. Third, a sufficient condition on the existence of state-feedback controller is provided in the form of Linear Matrix Inequality. Besides, convergence rate is obtained and the upper bound of the cost is calculated. Finally, effectiveness of the proposed method is verified via numerical example.