Stabilization for a class of switched nonlinear systems with time-varying delay under asynchronous switching

This paper considers the problem of exponential stabilization for a class of switched nonlinear systems with time-varying delay under asynchronous switching. Time delays appear not only in the state, but also in the switching signal of the controller. By construction of a novel Lyapunov-Krasovskii functional and combination with the average dwell time scheme, new sufficient conditions of exponential stabilization for a class of switching nonlinear systems are proposed in terms of linear matrix inequalities (LMIs). Moreover, the stabilizing feedback controllers with asynchronous switching are designed. Finally, a numerical example illustrates the effectiveness of the theoretical results.