Finite Time Stability Analysis Of Switched Singular Systems

With the continuous development of science and technology, in order to make the system get better control effect, the hybrid system has been widely concerned. In recent years, as the mainstream direction of hybrid system theory, switched systems achieved abundant research results. Most of the researches focused on the normal switched systems, less on switched singular systems. On the other hand, we usually study the Lyapunov stability of switched systems, namely the time is infinite. But in practical application, we are sometimes more concerned about the performance of the system within a finite time interval, that time is limited. Therefore, the research of the finite-time stability theory of switched singular systems is very necessary. Through the existing finite-time stability results of switched systems, this article discusses similar theory of the continuous time switched singular linear systems. The main contributions are as follows.The second chapter, finite-time stability and stabilization of continuous switched singular systems are studied. The standard switched singular systems is composed of several continuous or discrete singular systems according to the switching rules which regulate systems to run. Firstly, we discuss the solvability condition of the switched singular system. Secondly, by using mode-dependent average dwell time method and Lyapunov function method, we provide sufficient conditions to guaran-tee that the switched singular system is regular, impulse free, and finite-time stable or finite-time bounded. Then, we design the state feedback controllers to ensure that the closed-loop system is finite-time stable and finite-time bounded with a present H∞ disturbance attenuation level γ. Finally, numerical examples are given to verify the efficiency of the proposed theory.The third chapter, we discuss the finite-time stability for switched singular sys-tems with delay. First, with the help of Lyapunov-like function, sufficient conditions for finite-time stability and bounded of time-delay switched singular systems are proposed. Second, for robust time-delay switched singular systems, we give similar discuss. Third, we consider neutral switched singular systems. Using the average dwell time and Lyapunov-Krasovskii functional, we find asynchronous controllers such that the neutral switched singular systems is finite-time stability.Finally, summarize this article and look forward to the future.