Research On Guranteed Cost Control For Singular Systems With Uncertainty And Time-delay

Time-delay and uncertainty exist in all kinds of industral systems, such as communication systems, power systems. Singular nonlinear systems are discovered in many applied systems, such as constrained robot, hurricane forecast. Also, it is significant to do some research on nonlinear singular system with time-delay and uncertainty. So far the guranteed cost of normal systems has been perfect. For singular systems, they have few fruitful results. The guranteed cost of singular systems not only guranteed the stability amd meet the cost function, but also meet the condition of regular and impulse-free. So the guranteed cost control of singular systems is more complicated than that of normal systems. And time-delays exist in singular systems generally, such as data calculation, system varible mearsure, chemical process, obersevation delay.Currently the research on the guranteed cost of singular systems with time-delay gets some fruilful results. In1997, Keel and Bhattacharyya point the design method of robust (such as the complicated methods of H2、H∞and μ). The controller with parameter variation has a weak ability to maintain the systems stable. It is necessary that the rsearch that both the object with uncertainty and its own uncertainty are robust control, that is non-fragile guranteed cost. In this thesis, I do some research on the guranteed cost control and the H∞guranteed cost control for singular system with uncertainty and time-delay. Summarize the contents:Chapter one:it introduces the question, the method and the mind of research, and summaries the background briefly.Chapter two:it introduces the prepared knowledge used in this paper briefly:uncertainty description, LMI, stability, singular system with time-delay.Chapter three:the non-fragile guaranteed cost control problem for a class of uncertain singular systems with state delay and input delay is discussed. Based on linear matrix inequality method, the sufficient and necessary condition of non-fragile guaranteed cost and corresponding controller design are presented. A numerial example is given to illustrate the effectiveness of the design method.Chapter four:the design of robust H∞guaranteed cost controller was studied for a class for uncertain nonlinear singular systems with state delay based on the linear matrix inequality approach, a design approach and a suffient condition are presented for the existence of H∞guranteed cost controller. When these LMIS are feasible, an explicit expression of guranteed cost controller is obtained. Finally, a numberial example is presented to inllustrate the feasibility and validity of this approach.Chapter five:the guaranteed cost control problem for a class of uncertain singular systems with state delay is discussed. Based on linear matrix inequality methods, the sufficient and necessary condition of guaranteed cost and corresponding controller design are presented. A numerial example is given to illustrate the effectiveness of the design method.