Asymptotic Stability of Switched System with Time Delay: Comparison Theorem

This paper mainly considers the stability of switched system composed of linear subsystems with time delay. The equation solutions under a pointed switching sequence are shown firstly. Through movement analysis of the switched system, the stability condition of switched linear scalar system are given. Then after analyzing the movements of this system, the stability condition for the switched linear scalar system with time-delay is obtained again. Meantime, by using the Comparison Theorem, the result can be extended to the multidimensional case. Finally, simulation results are illustrated to show the effectiveness of our results.