Guaranteed Cost Control Of Singular System And Its Application In The Financial System

The basic idea of the guaranteed cost control is to design a controller such that the closed-loop system is asymptotically stable for all admissible uncertainties and the performance index of the closed-loop system is not more than a specified upper bound.In recent years,the problem of guaranteed cost control for uncertain systems has been studied extensively,and a lot of progress are obtained.However,so far,research on it is mainly confined to the normal systems.And for the guaranteed cost control of uncertain singular systems,especially in its application to practice,it is very hard to study owing to the particularity of its own.Thus,it is very meaningful to study the problem about guaranteed cost control of uncertain singular systems.In this paper,guaranteed cost control of uncertain singular systems and its applications in Finance are stressd.The main results in this dissertation are as follows:Firstly,the background related to the subject is summarized and some preliminary knowledge on LMI,matrix norm,lemmas and inequalities used in the dissertation are given.Secondly,the problems of guaranteed cost control and reliable guaranteed cost control for uncertain continuous singular systems are studied by generalized Ricatti equation,and the existence condition of the guaranteed cost controller is obtained.By converting the dynamic adjustment model of portfolio to uncertain continuous singular systems and by converting the failure of the transaction to the failure of the systems' actuator,the example analysis is carried out with the guaranteed cost controller obtained.Thirdly,the problems of guaranteed cost control for uncertain discrete-time singular systems are studied by generalized Ricatti equation,and the existence condition of the guaranteed cost controller is obtained.By converting the dynamic adjustment model of the banks' asset portfolio to uncertain discrete-time singular systems,the example analysis and the simulation are carried out with the guaranteed cost controller obtained.The last section summarizes the main work in this paper,and prospects the research of the guaranteed cost control for uncertain singular systems based on the shortcomings.