ℓ2 gain analysis and state feedback stabilization of switched systems with multiple additive time-varying delays

This paper focuses on the problem of ℓ2 gain analysis and state feedback stabilization for a class of switched systems with multiple additive time-varying delays. First, a new model about switched systems with multiple additive time-varying delays is given. Then, based on the extended dynamic delay interval (EDDI) method, we construct a new multiple Lyapunov function. Combing average dwell-time method, reciprocally convex combination technique and Wirtinger interval inequality to estimate the bounding of the integral term, the stability criteria and ℓ2 gain performance of switched systems are given. At last, based on the stability results, the state feedback stabilization problem of the switched systems is studied. The results of sufficient conditions are shown in terms of linear matrix inequalities (LMIs). Numerical examples are provided to show the effectiveness of the proposed methods.