Finite Time Stability Of A Class Of Singular Cascade Switched Systems With Time Delay

Switched system is an important hybrid system,which is composed of several sub-systems and switching rules acting on them.If every subsystem of a switched system is a singular system,it is called a singular switched system.The research on switched systems and singular switched systems has attracted more and more attention for the extensive application.However,the research results on the singular cascade switched systems with time delay or the singular cascade switched systems with interference are very limited.In this paper,the finite time stability and finite time bounded problem of a class of singular cascade switched systems with time delay are studied by using single Lyapunov function,multiple Lyapunov function and the properties of convex combination.The main contents are as follows:Firstly,the finite time stability problem of singular cascade switched systems with time delay is discussed.By means of single Lyapunov function method,the state feedback controller and the switching law are designed,and the sufficient conditions which ensure the finite time stability of the switched systems are obtained.Secondly,the finite time bounded problem of singular cascade switched systems with time delay is discussed.By using the method of single Lyapunov function and the proper-ties of convex combination,the switching signal and the state feedback controller are de-signed,and the sufficient conditions which ensure the finite time boundary of the switched systems are obtained.At last.the finite time bounded problem of singular cascade switched systems with time delay is discussed.By using multiple Lyapunov function method,the state feedback controller and the switching law are designed,to obtain sufficient conditions for the finite time bounded problem of the switched systems.