Study Of Dissipative Analysis And Control Problem For Singular Time-Delay Systems

Time delays often occur in many practical and engineering fields and they are often sources of instability and degradation in control systems, so the study of time-delay systems is important both in theory and in practice, and has thus been of great interest to a large number of researchers in the last few decades. On the other hand, singular system is a kind of dynamic system of more general form and abroad applied background. Dissipative theory plays an important role in the stability research of control systems, the implication is that there exists a nonnegative energy function (namely store function) such that the energy consumption of a control system is always less than the supply rate of the energy. Up to now, very few papers have investigated the dissipative analysis and control problem of singular systems with interval time-varying delays, which remains open but challenging.The thesis discusses on the dissipative control problem for singular systems with constant delay and time-varying delay, the main contribution of this thesis is summarized as follows:(1) The main background of the problem discussed in this thesis is introduced. Firstly, the structure characteristics and recent progress for singular systems and singular systems with time-delay are introduced. Then the significance, application background and the recent progress are presented for the theory of dissipative.(2) The mathematical definitions for dissipative singular systems are introduced. Afterwards, the relevant handling methods and lemmas related to the research contents are introduced in this article.(3) The dissipative analysis for continuous singular time-delay systems with constant delay is studied, the LMI conditions of dissipative for singular systems with time-delay are derived. And the conditions for the closed-loop systems to be admissible and strictly dissipative are proposed in the cases of memory-less state feed-back controller.(4) For the singular time-delay systems with time-varying delay, the dissipative control problems are studied by using a general Lyapunov-Krasovskii function. On this basis, a less conservative method by using non-uniform time-delay decomposition is proposed. By constructing new complete delay-decomposing Lyapunov-Krasovskii functions and employing the improved free-weighting matrices method, the LMI conditions of dissipative for the systems are derived. Then, on the basis, the conditions for the closed-loop systems to be admissible and strictly dissipative are proposed in the cases of memory-less state feed-back controller.(5) A summary of this paper is given. At the same time, we give an expectation for the future work.As the conclusions obtained in the thesis, simulation examples are presented to show the feasibility and effectiveness of the proposed methods.