Dissertation
Dissertation > Mathematical sciences and chemical > Mathematics > Control theory, information theory ( mathematical theory ) > Cybernetics ( control theory, mathematical theory )

Robust H_∞Control for Singular Systems with Multiple Time-delays

Author FengZuo
Tutor ZhangXiuHua
School Northeastern University
Course Operational Research and Cybernetics
Keywords systems with multiple time-delays Lyapunov function asymptoticalstability free weighting matrices robust H_∞control
CLC O231
Type Master's thesis
Year 2013
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Singular systems theory has been developed profoundly since its beginning. Recently the singular systems with uncertainty and time-delay have been paid special attention by the researchers because of comprehensive practical application background. Furthermore, delay is the root induced instability, so the research of robust stability analysis and controller’s designing for delayed systems is the major topic. Thereby, according to the complexion at the present time, the problems of robust H∞control for uncertain singular system with multiple time-delays has been discussed in this paper. Based on a Lyapunov functional method and sufficient conditions for robust stability in terms of linear matrix inequality(LMI), the conditions of the stability of considering systems can be got. The main conclusions in this paper are:(1) The background, the development of the theory and recent research achievements of singular systems with uncertainty and time-delay, and H∞robust control are introduced respectively. In addition, the method-free weighing matrices that used in this paper is introduced.(2) The definitions of stability of the singular systems, singular systems with time delays, the basic knowledge of H∞control theory, and some basic commonly mathematical inequalities used in this paper are introduced.(3) The problem of asymptotic stability of singular systems with two-time-delays has been studied by two methods. First of all, by means of Lyapunov function, then free weighing matrices is introduced, and the asymptotic stability of the systems is analyzed. Based on which, a sufficient condition is presented such that the system is asymptotically stable. (4) The problems of H∞control for singular systems with multiple time-delays of certain and uncertain are studied respectively. Using the method dealing with normal systems containing time-delay, we studied the asymptotic stability and the performance of robust H∞control of the systems. Then, we got a sufficient condition for the existence of a memoryless H∞state-feedback controller. And based on which, the corresponding state feedback controller had been designed. Last, the examples are given in the end correspondingly to prove the effectiveness of the conclusions.

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