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Stability And Control Of Time-Delay Systems: Further Analysis And Research

Posted on:2012-08-16Degree:DoctorType:Dissertation
Country:ChinaCandidate:B Y ZhangFull Text:PDF
GTID:1118330335486516Subject:Control Science and Engineering
Abstract/Summary:PDF Full Text Request
Time-delay system is one of the fundamental research branches in the theory of control systems, which has received considerable attention. Time-delay systems are infinite dimen-sional, and thus it is always difficult to deeply analyze and study such systems. As there is no universal method or theory, it is necessary to study the time-delay systems and control problems by developing particular methods. On the basis of the existing studies and by im-proving the methods proposed in the literature, this dissertation presents some new results on a series of important time-delay systems and control problems. These results are generally less conservative than some of the existing ones in the literature. The contributions of this dissertation are summarized as follows:1. The problems of stability analysis for three classes of neural networks with time-varying delays are investigated. Firstly, neuron activation functions are assumed to satisfy a rel-atively week constraint. Under such an assumption, a set of inequalities are obtained for any positive-definite diagonal matrices, which play an important role in decreasing the conservatism of the desired results. Then, appropriate Lyapunov-Krasovskii functionals are employed to derive delay-dependent conditions guaranteeing the global exponential stability for the considered systems. These conditions are expressed in terms of lin-ear matrix inequalities (LMIs). Numerical examples show that the results given in this dissertation are less conservative than some of the existing ones in the literature.2. The problems of stability analysis and H∞control for linear neutral systems with dis-tributed delays are investigated. Firstly, by employing an appropriate Lyapunov-Krasovskii functional and applying Jensen's inequality, delay-dependent stability criteria are ob-tained in terms of LMIs, which improve the exiting results. Secondly, new results on the existence of state-feedback H∞controllers are obtained, and the controller design method is proposed. The designed controllers ensure that the closed-loop system is asymptotically stable with a prescribed H∞disturbance attenuation level. A numerical example is provided to demonstrate the effectiveness of the proposed design method.3. The problem of stability analysis for discrete-time linear systems with time-varying de-lays is investigated. A Lyapunov-Krasovskii functional that has more general form is employed, and less conservative delay-dependent stability criteria are obtained. The advantages of these criteria are demonstrated by a numerical example. Based on this, the problem of state-feedback memory controller design is considered for discrete-time linear systems. A delay-dependent result on the existence of desired controllers is ob-tained, and the controller design method is presented. A numerical example is provided to demonstrate the effectiveness of the proposed design method.4. The problems of stability analysis, stabilization with input saturation, passivity analysis and passification for continuous-time Markovian jump systems with time-varying de-lays are investigated. Firstly, the exiting construction approach for Lyapunov-Krasovskii functionals is improved by using mode-dependent positive-definite matrices in the dou-ble integral terms of Lyapunov-Krasovskii functionals, and then, delay-dependent sta-bility criteria are obtained. Furthermore, delay-dependent results for the solvability of the problem of stabilization with input saturation, and effective design methods for de-sired state-feedback controllers and dynamic output-feedback controllers are developed. Finally, existence conditions and design methods for state-feedback passive controllers and output-feedback passive controllers are presented, respectively. Numerical exam-ples are provided to illustrate the effectiveness of the proposed design methods.5. For fuzzy systems with constant delays, the problem of robust stabilization with expo-nential estimate is investigated. A new method for fuzzy control design is proposed based on simplified LMIs. Based on such a method, the numbers of LMIs and decision variables in fuzzy control design results are distinctly reduced, and thus the computa-tional cost is reduced correspondingly and the obtained results are easy to apply. By using this new method, delay-dependent results on the existence of state-feedback fuzzy controllers are obtained. These results are dependent not only on the size of the delays, but also on the exponential decay rate. This fact enables one to design fuzzy controllers by selecting decay rates according to practical requirements. The desired controllers can be obtained by solving a set of LMIs. Numerical examples are provided to demonstrate the effectiveness of the proposed design methods.6. For fuzzy systems with time-varying delays, the problems of state-feedback fuzzy con-troller design under different performance constraints are investigated. Firstly, for the case of continuous-time systems, the passivity analysis and passive control are stud-ied. Delay-dependent results on the existence of state-feedback fuzzy controllers are obtained in terms of LMIs. The design method is also provided. Secondly, for the case of discrete-time systems, the robust H∞control and generalized H2 control are considered. By employing fuzzy-basis-dependent Lyapunov-Krasovskii functionals and applying the relaxed LMI approach, delay-dependent results on the existence of desired controllers are obtained. The design method for desired controllers is also presented. Examples are provided to demonstrate the effectiveness of the proposed methods.
Keywords/Search Tags:Time-delay systems, Delay-dependent conditions, Neural networks, Marko-vian jump systems, Fuzzy systems, Passive control, H_∞control, Generalized H2 control
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