Robust stability and H∞ control for nonlinear discrete-time switched systems with interval time-varying delay

This paper considers the problems of the robust stability analysis and H-infinity controller synthesis for uncertain discrete-time switched systems with interval time-varying delay and nonlinear disturbances. Based on the system transformation and by introducing a switched Lyapunov-Krasovskii functional, the novel sufficient conditions, which guarantee that the uncertain discrete-time switched system is robust asymptotically stable are obtained in terms of linear matrix inequalities. Then, the robust H-infinity control synthesis via switched state feedback is studied for a class of discrete-time switched systems with uncertainties and nonlinear disturbances. We designed a switched state feedback controller to stabilize asymptotically discrete-time switched systems with interval time-varying delay and H-infinity disturbance attenuation level based on matrix inequality conditions. Examples are provided to illustrate the advantage and effectiveness of the proposed method.