Analysis of robust stability for switched systems with multiple time-delays

The sufficient conditions of delay-dependent exponential stability for switched systems and robust exponential stability for uncertain switched systems with two time-delays are presented by using average dwell time method and free-weighting matrix method. The interaction between different time-delays is considered. The sufficient conditions do not need that every subsystem is stable. The designed methods of the switching law are also given. The sufficient conditions are given in the form of linear matrix inequalities that can be solved easily. The result is proven to be valid by the simulation at last.