Robust Control For Time-delay Singular System

Singular system is a kind of dynamic system of more general form and abroad applied background. It has been developed sufficiently from 1970s, and many results in the normal system have been extended to singular systems. Since delay often occurs in many practical and engineering fields, the research of delay system has attracted much interest in recent years. Singular systems contain many singular systems with time-delay which are the more general systems than normal systems. Sometimes normal systems are the particular case of them and some problems only can be described by time-delay singular systems. There have been a lot of achievements on the stability and the basic theories, but robust control problem is less than it, many control problems also need continue research about them.The theory of H_∞ control originated early in 1980s. Since it has remedied the shortage of control theory in practical application and the wide applicability of the model, it has been attached important and developed into one of the most important aspect for the control theory. In recent years, the research of H_∞ control for normal systems has been developed sufficiently, all kinds of method to design H_∞ controller is put forward one after the other. In this paper, at the base of the singular system control theory and the robust control theory for normal systems, we discuss the problem of robust H_∞ control, guarantee cost control and the application in economy. The paper is constructed as follows:(1) The main background is introduced for this paper. First, the background and description for singular systems and delay system is introduced, then discuss the recent develop for H_∞ control and guaranteed cost control etc. Many practical examples are given to illustrate the wide existence of such systems in engineering.(2) The problems of stability, robust guaranteed cost control and H_∞ control etc are discussed for neutral systems. The conclusion which the existence condition of the stability and H_∞ control with delay-dependent, dynamic output feedback H_∞ control and the design of guaranteed cost controller with disturbance attenuation H_∞ performance are obtained by showing the equivalent to the feasibility of some linear matrix inequality.(3) A bounded real lemma and the method of LMI are derived by the sufficient...