Exponential stability of time-delay feedback switched systems in the presence of asynchronous switching

This paper studies the asynchronously switched state time-delay feedback control problem for a class of switched linear systems with average dwell time. Using extended multiple Lyapunov-like functional, we first investigate the stability of a class of switched time-delay nonlinear systems with average dwell time. Then, based on this result, sufficient conditions for exponential stability are developed for time-delay feedback switched linear systems in the presence of asynchronous switching, where “asynchronous” means the switching of the controllers has a lag to the switching of subsystems. These conditions are provided in terms of linear matrix inequalities (LMIs). A numerical example is presented to illustrate the developed results.