Reduce-order H_∞ Filtering Design For Uncertain Time-delays Singular Systems

In this paper, we study problems of the H∞reduce-order filtering for uncertain continuous singular systems and discrete singular systems. By means of linear matrix inequalities, a sufficient condition for the existence of a H∞reduce-order filtering is given. The design method for the controller is provided for the solutions of matrix inequalities. Dynamic output feedback control and H∞filtering are dual control problems. So use the same method, we address the existence condition and the design method of guaranteed cost controller for a given disturbance attenuation H∞performanceγ. The examples are given correspondingly to prove the effectiveness of the conclusions.The main content of this paper is as follows:In chapter 2, the H∞reduce-order filtering for continuous singular systems with structured uncertainties is considered. Firstly, using the method of singular Lyapunov function and Lyapunov equation, sufficient condition in terms of LMIs for the existence of H∞reduce-order controllers is obtained for all the admissible uncertainties of systems and disturbances of controllers, such that the time-delay singular closed-loop system satisfies a prescribed H∞performance and the stability of zero solution. At last the numerical example is given to illustrate the designed method.In chapter 3, the design of H∞controller is discussed for time-delay discrete singular systems with parameter uncertainties. Firstly, by means of generalized Lyapunov function and linear matrix inequality (LMI), the stability with zero solution is studied for the system, and a sufficient condition is given such that the system is stable with zero solution and also a H∞norm constraint. And a H∞reduce-order filtering is designed to guarantee stability and the performance of the resultant closed-loop system. In chapter 4, passive filtering for a class of linear uncertain descriptor time-delay systems is proposed. By means of linear matrix inequality (LMI), the parameter uncertainties of the system are norm bounded. The proposed designed method is given by doing the feasible solution problem of linear matrix inequalities. The objective is to design passive filtering, such that the closed-loop system is admission and satisfies the proposed passive performance.In chapter 5, the problem of H∞guaranteed cost control was discussed for a class of uncertain descriptor systems. By using the linear matrix inequality approach, a sufficient condition for the existence of dynamic output feedback guaranteed cost controller is given, such that the closed-loop system satisfies a prescribed H∞performance. A numerical example is given to illustrate the feasibility of the designed method.