Stability Analysis For Switched Systems With Time Delay

As a special kind of hybrid systems, switched systems are made by a team of continuous subsystems (or discrete subsystems) and switching rules which can coordinate the switch between one subsystem and another subsystem. It has been attracted extensive attention in recent years. However, in practical engineering system, delay phenomenon generally exists. The system becomes complicated because of the delay .Meanwhile, it tend to affect the performance of the system, especially stability. Therefore, the analysis and comprehensive research of the delay switched systems have very important practical significance.The stability and performance of the switched delay systems are discussed in this paper. The main work is summarized as follows:Firstly, we study the stability problem of a class of delay perturbation switched systems and performance of H∞in this paper. We design the switching lawσ(t ) for varying delays and constant delay case by the use of multiple Lyapunov function method. This paper gets the corresponding sufficient conditions for asymptotic stability of the systems and the performance indexγwhich can meet H∞.Secondly, it is studied that a class of uncertain nonlinear delay switched systems in this paper. When the nonlinear item meet some constraint conditions, we design the switching lawσ(t ) for varying delays and constant delay case by the use of single Lyapunov function method. We get the sufficient conditions for the systems which are asymptotic stabilized and can meet H∞performance indexγunder the corresponding switching lawσ(t ).In the finality, we summarize the full text, as well as the focus of the next step.