Stability Analysis And Robust H_? Filter Design For Linear Systems With Time-varying Delays

There always exist time-delayed factors in the real systems due to the processes for the transmission of energies,materials and data,which influence the dynamical behavior of the systems.Therefore,the time-delayed model can more preciously describe the dynamical characteristics of the various natural and social engineering systems,and the relative control theory of time-delayed systems is the current research hot-spots.In this dissertation,the stability analysis and the robust H_?filter design will be investigated for the linear systems with time-varying delays.New methods and approaches for the stability analysis and the robust H_?filter design will be developed in order to lessen the conservativeness of the stability criteria and explore the influence of time delays on systems stability.The stability analysis based on the Lyapunov-Razumikhin theorem,the Lyapunov-Krasovskii theorem will be mainly explored.Based on the two kinds of stability analysis,the corresponding stability criteria will be established and then new approaches for the robust H_?filter design will be also proposed by the obtained stability criteria.The obtained results in this dissertation will further develop the theory for the linear systems with time-varying delays and provide theoretical basis for the social and engineering practices.The main contributions of the dissertation are summarized as follow:1.The background,research significance and current state of the topic in the dissertation are reviewed.In addition,some preliminaries are presented,which including some notations,definitions and lemmas.Finally,some methods for the time-delayed systems are briefly discussed.2.The stability of a type of the linear systems with time-varying delays is investigated.Based on the Lyapunov-Razumikhin theorem and the Newton-Leibniz formula,a new Razumikhin-type stability criteria is established,which is described by algebra Lyapunov matrix equation rather than LMI,with advantages of simple form and less computation.In addition,the criteria shows that the delayed term isn't only a disturbance of the systems stability,but also a positive contribution to the systems stability.Finally,three examples are given to illustrate the efficiency and the correctness of the obtained results.3.Based on the Lyapunov-Krasovskii theorem,the stability of a type of the linear systems with time-varying delays is developed.A new Lyapunov functional with a quadruple integral quadratic terms is proposed,and then a new stability criteria is established with advantages of less conservativeness under some algebraic operations.Finally,two examples are given to illustrate the efficiency and the correctness of the established stability criteria.4.The robust H_?filters for a type of the linear systems with time-varying delays are designed.Two design methods for robust H_?filters are established based on the Lyapunov-Rzumikhin method and the Lyapunov-Krasovskii method,respectively.Among of them,Razumikhin-type method is described by algebraic Riccati matrix equation with advantages of simple form and less computaion;Krasovskii-type method is described by LMI,and the filter gain is got easily by solving the LMI.Finally,two examples are given to illustrate the usage and the efficiency of the proposed method.In the dissertation,aiming at the difficulties brought about by time delays and achieving the target to less conservativeness of the stability criteria,some new explorations about the positive effect of time delays on systems stability are launched.By virtue of relevant mathematical principles,methods and tools,the Lyapunov-Razumikhin theorem and the Lyapunov-Krasovskii theorem are used to overcome difficulties in our direction and tried to make some progress in the related control theory of the linear systems with time-varying delays.