Robust exponential stability for switched systems with interval time-varying delay

Stability criteria and design of hybrid controllers for a class of switched systems with interval time-varying delay are considered in this paper. Based on taking both the lower bound and upper bound of delay into consideration in the chosen piecewise Lyapunov-Krasovskii functional, we investigate the exponential stability by the method of average dwell time. A new delay-rang-dependent stability criteria and stabilization conditions are derived in terms of linear matrix inequalities. Then based on this condition, the hybrid state feedback controller is designed and the robust exponential stability is also proposed. Moreover, in order to obtain much less conservative results, the integral inequality and reciprocally convex approach are introduced. Finally, the numerical example is given to demonstrate the applicability and the effectiveness of the proposed method.