Study On Guaranteed Cost Control Of Singular Systems

The basic idea of the guaranteed cost control approach is to design a controller such that the closed—loop system is asymptotically stable for all admissible uncertainties and the closed—loop cost function value is not more than a specified upper bound. Although, many significant guaranteed cost results have been presented in the linear systems, there has been few valid system analysis and synthetic methods. And the guaranteed cost control methods about the uncertain system with inequality—enlarging technology exist some conservativity, some of them are very serious. On the other hand, singular systems have very important application in the field of economic management. Dynamic input—output model is the typical singular system model, it plays an important role in our contry's market economy. Thus, it is meaningful to study the problem about guaranteed cost control of the uncertain singular systems theoretically and practically.In this paper, guaranteed cost control for singular systems are stressed. The main results in this dissertation are as follows:Firstly, the present status of the guaranteed cost control is discribed, and the Basic knowledge and Prearaory lemmas about the continuous and discrete singular systems are given.Secondly, the problems of guaranteed cost control for uncertain contiuous and discrete singular systems are studied by LMI, Lyapunov function and Spectral norm. And the condition that existing the guaranteed cost controller for the closed—loop systems is obtained. For the performance index of the singular system, it designs a class of controllers such that the closed—loop system is asymptotically stable and the cost function value is not more than a specified upper bound, then presents the appliance for the discrete guaranteed cost control in the input—output model.Thirdly, for the state is not measured, guarnteed cost control of linear uncertain singular systems based on the state observer is discussed. The condition and parameter expression of the guaranteed cost control are obtained by LMI, generalized algebraic Riccati inequality and Lyapunov function. The last section summarizes the main work in this paper and prospects the research of uncertain guaranteed cost control problems in the future.