State Feedback H_∞ Control For Singular Time-delay Systems

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 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 singular time-delay systems, so the research on them is of theoretical and practical importance. In this paper, the H_∞control problems of the state feedback of the singular time-delay systems are studied respectively, by means of LMI method.First, the memory-less H_∞sate-feedback controller of the singular time-delay systems with state delays is researched. A sufficient condition that can make system admissible and satisfies H_∞performance index is obtained, the H_∞state-feedback controller, which satisfies the requirement of the design, is obtained by solving the corresponding LMI. Lastly, a numerical example is given to illustrate the probability of the proposed method.Next, the memory-less H_∞sate-feedback controller of the singular time-delay systems with state and input delays is researched. A sufficient condition that can make system admissible and satisfies H_∞performance index is obtained. Based on LMI and proper Lyapunov functions, the H_∞state-feedback controller that can make closed-loop system admissible and satisfies H_∞performance index can be obtained by solving the corresponding LMI. At last, a numerical example is presented to illustrate the validity of this approach.Finally, the memory H_∞sate-feedback controller of the singular time-delay systems with state delays is researched. The H_∞state-feedback controller, which satisfies the requirement of the design, is obtained by solving the corresponding LMI. Lastly, a numerical example is given to illustrate the probability of the proposed method.