Robust stability of uncertain discrete-time switched systems with time-varying delay

In this paper we focus on robust stability for uncertain discrete-time switched Systems with Time-varying Delay and linear fractional perturbations for arbitrary switching law. Firstly, a new matrix inequality considering uncertainties is introduced and proved. By means of it, new sufficient conditions of asymptotic stability for nominal switched system are proposed by using switched Lyapunov function. The conditions are dependent on the minimum and maximum delay bounds and are established in a form of a set of strict linear matrix inequalities (LMIs). Furthermore, slack variables are introduced for more relaxation. Finally, some numerical examples are provided to demonstrate the effectiveness of the proposed approach and to compare the obtained results with the existing literature ones.