Exponential stabilization of nonlinear switched systems with distributed time-delay: An average dwell time approach

In this paper, the exponential stabilization problem is discussed for nonlinear switched systems subject to the distributed time-delay. Attention is focused on the design of a state feedback controller such that, the closed-loop system is exponentially stable with a guaranteed weighted L2 gain. By resorting to the average dwell time method and the piecewise Lyapunov functional approach, sufficient conditions are derived for the solvability of the addressed problem in terms of the feasibility of certain Hamilton-Jacobi inequalities (HJIs). The explicit expression of the desired controller is formulated via solving the presented set of HJIs. Furthermore, within the proposed framework, the exponential stabilization problems are investigated, respectively, for nonlinear switched systems with mixed time-delays and linear switched systems with the distributed time-delay. Finally, a simulation example is given to illustrate the effectiveness and applicability of the proposed algorithm.