Asynchronous control of discrete-time switched systems with non-linear perturbation

This paper is concerned with the asynchronous control problem for a class of discrete-time switched systems with non-linear perturbation. The asynchronous switching means that the switching signal of the controller experiences a time delay with respect to that of the system. The analytical solution of the state equation for the asynchronously switched system is utilized to study the dynamics of the system directly without constructing the Lyapunov function. By using the average dwell time approach, sufficient conditions for exponential stability of a closed-loop system are established. Moreover, asynchronously switched controllers are designed in terms of linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.