The Stability Analysis And Guaranteed Cost Control Of Switched Singular System

Switched singular system is a special class of hybrid system, it is composed of subsystems, and subsystems are singular systems. the switched singular system is a class of very complex system, it is more difficult to study them, we must consider many problems. In this paper, we study a kind of simple switched linear singular systems, they are regular and no impulse, and there is no state jump at switching time.Stability is an important characteristic of the system.A system can be able to work normally, it must be a stable system. Switched system can be considered as that consists of a group of subsystems and the switching signal.The stability of subsystems are not equivalent to the stability of the entire switched system. We mainly consider the autonomous switched singular systems. We find a common Lyapunov function to make the whole system satisfy some conditions, so the system is stable. We also base on the quadratic stability, to the quadratic stability, choose a quadratic positive-definite function which is similar to the common Lyapunov function. We study continuous switched singular systems in the second part and discrete singular systems in the third part. We give an example in eyery part, and indicate that the discrimination method is effective.The robust stabilization problem of uncertain system with norm-bounded has been studied extensively, and achieved many significant results. But for a practical system, only having stability is not enough, we need to consider other performances. In this paper, on the base of guaranteed cost control theories and relevant researches of switched systems, we study the guaranteed cost control problem of switched singular system with uncertain items in the system matrices and input matrices. By Lyapunov function method, we get the sufficient conditions of guaranteed cost control of switched singular system with state-feedback. The sufficient condition of existing guaranteed cost control under arbitrary switching laws is given, the condition in the form of LMI and the parameterized representation and performance index are shown. To the autonomous system of no control input, we derive the condition of existing guaranteed cost control. We study guaranteed cost control of continuous switched singular system in the fourth part and guaranteed cost control of discrete switched singular system in the fifth part.