Admissibility Analysis And Control Of Singular Time-Delay Systems

Time delay is widely found in a variety of systems such as physical systems, biological systems and industrial systems. It makes the analysis and synthesis of systems more complicated, and it is often a source of instability and degradation of performances for the systems. As the dynamic systems, singular systems have more extensive uses than regular ones and can better describe the physical systems than regular ones. The models of singular systems are widely found in power systems, eco-nomic systems, robot systems, aerospace engineering and biological systems. Thus, study of singular systems is important in practice. Admissibility is the fundamental requirement for the analysis and synthesis of singular systems, so the topic of this dissertation is of great value to theory study.In terms of linear matrix inequality technique and by the second method of Lyapunov, this dissertation investigates the admissibility analysis and control of singular time-delay systems. The main contents include:admissibility analysis and controller design respectively for continuous singular time-delay systems and discrete singular time-delay systems with constant delay; H∞control of discrete singular time-delay systems with constant delay; admissibility analysis and control of discrete singular time-delay systems with interval time-varying delay. This dissertation is organized as follows:(1) Firstly, the background and the development of singular systems are in-troduced. Secondly, the survey of time-delay systems is shown briefly. Thirdly, the current research status of singular time-delay systems are enumerated:admissibility analysis and control, H∞control, guaranteed cost control, state observer design, H∞filtering design, Markovian jump systems and other control problems. Furthermore, the unsolved problems of singular time-delay systems are illustrated and the research significance is given. Finally, the main work of this dissertation is presented.(2) The admissibility analysis and controller design for continuous singular time-delay systems with constant delay and norm-bounded uncertainty are studied in two ways. The first method is proved to improve the existing results by choosing a Lyapunov-Krasovskii functional with less conservatism. The theoretical and numer-ical results are shown to demonstrate that the proposed methods are less conserva-tive than the existing ones. By utilizing Jensen’s inequality, a new delay-dependent admissibility condition is established. Compared with the existing results, the con-servatism is equivalent and the computational complexity is less. At the same time, two proposed methods are compared with each other and a numerical example is employed to show that the second method is less conservative than the first one. Both of the methods give the state feedback controller design to ensure that the closed-loop systems are robustly admissible for the uncertainties.(3) Delay-independent and delay-dependent admissibility conditions of discrete singular time-delay systems with constant delay are presented respectively. On the basis of the results, utilizing matrix theory, a new approach to designing the state feedback controller is proposed to ensure that the closed-loop system is admissible. By comparisons with the existing results, the proposed delay-dependent admissibil-ity condition is proved to be less conservative and less computational complexity.(4) Delay-independent and delay-dependent H∞control of discrete singular time-delay systems with constant delay and disturbance input are studied respec-tively. A delay-independent bounded real lemma and a delay-dependent bounded real lemma are given respectively. On the basis of the results, utilizing matrix the-ory, two state feedback H∞controller are designed correspondingly such that the closed-loop systems are not only admissible, but also satisfying the given H∞per-formance. By comparisons with the existing results via a numerical example, the proposed methods are proved to be superior.(5) Admissibility analysis and controller design for discrete singular time-delay systems with interval time-varying delay are studied. The lower and the up-per bounds of the interval delay are fully considered in constructing Lyapunov-Krasovskii functional and Jensen’s inequality is utilized, then a delay-dependent admissibility condition relevant to the bounds of interval delay is established. A nu-merical example is employed to show that the proposed method is less conservative than the existing ones. Then, the results are applied to regular systems, and some lemmas are obtained. A numerical example is employed to show that the lemmas are less conservative than the existing ones. On the basis of the results, utilizing matrix theory, a new approach to designing the state feedback controller is proposed to ensure that the closed-loop system is admissible.Finally, the prime work of the dissertation is summarized and some problems to be studied and the prospects in the future are proposed.