Research Of The Robust Control Of The Descriptor Interval System And The Finite Time Stability Of The Descriptor System

The stability of descriptor systems is one of the most important performance indexes for the descriptor system's model. In addition to the impulse moving model, The descriptor system also have exponential moving model, and so, the research of the stability of descriptor systems is more complex than that of normal systems. Generally the stability of descriptor systems is studied by converting it into normal systems. In the recent years, Zhang Qinglin and other scholars have generalized the Lyapunov stability theory of normal systems to descriptor systems, that is to say they use Lyapunov equation and Lyapunov inequality to study the stability problem of descriptor systems.The interval system are one of the complex system models with uncertain parameters. The elements of the system matrix for interval systems are not invariable constants, but variable on some fixed intervals. Recently, some results about the robust stability of normal interval systems have been gained. On the basis of Riccati inequality, the robust stability, the robust stabilization and the H_∞performance of normal interval systems have been investigated by Shi zhongke in 2003. By means of the inequality of linear matrix, the LMI conditions of the robust stability for uncertain systems have been obtained by Yu Li and Xu Shengyuan.On the basis of the Lyapunov stability theory of descriptor systems, the present paper first converts the interval system into the uncertain system, also, the robust stability, the robust stabilization and H_∞control problems have been studied by means of the methods for uncertain systems with parameter, furthermore, the problems of robust stability for descriptor interval systems with time delay and R-stabilization of descriptor interval systems have been researched.The mostly content of this paper as below:(1)In chapter 2, the Lyapunov inequality of descriptor systems has been gained. On the basis of these results, the correlative results of normal interval systems have been extended to descriptor interval system. At last, the robust stability of descriptor interval systems with time delay has been investigated. (2)In chapter 3, the necessary and sufficient condition of stabilization for descriptor systems with control time delay have been gained. Afterward, the necessary and sufficient condition of R-stabilization for the descriptor interval systems with control time delay has been obtained, on the basis of these results.(3)In chapter 4, the definition of finite-time stability about normal systems has been extended to descriptor systems and the the necessary and sufficient condition of finite-time stability of descriptor systems has been obtained. At last the state feedback about finite-time stability has been studied.