Robust stability of uncertain discrete-time switched systems with time-varying delay by Wirtinger Inequality via a switching signal design

This paper is concerned with the problem of robust stability for a class of linear switched discrete-time systems with time-varying delay and linear fractional perturbations parametric uncertainties, through a switching signal design. At first, by considering the uncertainties, new matrix inequality is introduced and proved. By means of that, new sufficient conditions guaranteeing the asymptotic stability of the studied system are proposed by constructing a novel Lyapunov-Krasovskii function, by using some linear matrix inequalities (LMIs) and by designing an appropriate switching signal. Furthermore, the discrete Wirtinger inequality approach is used to develop our approach and to improve less conservative results over than some recent research works. At last, numerical examples are proposed to verify the effectiveness and the merits of the proposed method and to compare the obtained results with some previous works in the literature.