Delay-dependent exponential stability for switched delay systems

Delay-dependent exponential stability criteria are presented for switched systems consisting of a family of stable and unstable subsystems with interval time-varying delay. Two cases with regard to such delay are considered: one is that time-varying delay function is differentiable and bounded and the other is that time-varying delay function is continuous and bounded. It is very difficult to analyze the stability of such systems due to the existence of time delay and unstable subsystems. By introducing some free-weighting matrices, constructing the new Lyapunov–Krasovskii functional and taking advantage of the average dwell time technique, not only is this difficulty overcome but also sufficient conditions for such criteria are obtained and formulated in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness and feasibility of the proposed approache