The Stability,Control And Filtering For Some Classes Of Differential Systems With Time Delays

In the dynamical systems, delays are always exist. In addition, almost of all systems may suffer uncertainties for the practical industrial process, such as unmodeled dynamics, structured parametric uncertainties, change of the operating environment, model reduction and linearization approximations and external disturbances uncertainties, etc. In the application, control systems stability and performance are always required, but the primary factors that dominate systems stability include delays and uncertainties. Therefore, it is necessary to consider the problems of robust control and filtering for uncertain systems with time-delay. On the other hand, as an exceptional case of delay systems, neutral differential systems are significant both in theory and in practice, the research of stability set store by scholars of the domestic and overseas.Based on Lyapunov stability theory and matrix theory, and through establishing proper Lyapunov function, Lyapunov- Krasovskii functional method and linear matrix inequality are adopted in this thesis, the designing of robust optimal H∞controllers for uncertain systems , H∞filtering for delay systems and the stability for a class of neutral differential equations are studied. The main contents are as follows:1. For some classes of uncertain time-varying linear systems with time-delay, the analysis and design of robust optimal H∞controllers are studied. The sufficient conditions of existence of H∞feedback controllers are obtained by using integral inequality and free-weighting matrix method. Based on the linear matrix inequality(LMI) approach, the sufficient conditions could be transformed to LMIs. The optimal controllers are easily constructed by the feasible solutions. The obtained controllers guarantee the robust stability and H∞performance of the resulting closed-loop systems. The stabilization conditions depend on size of delays and require no information about the derivate of time delays, which can be used to deal with the systems with fast time-varying delay. Finally, some examples are presented to illustrate the effectiveness and superiority of the design method by using Matlab tool box.2. The problem of H∞filters design for two classes of delay systems is concered in this thesis. Based on Lyapunov- Krasovskii functional method and following the free-weighing matrix lines, the H∞filters are presented in terms of linear matrix inequality(LMI). The designed filters ensure that the filtering error dynamics are stable with prescribed disturbance attenuation degree. The new delay-dependent sufficient conditions for the existence of H∞filters are derived. The examples show the feasibility of the approach.3. For a class of neutral differential equations which contain both multiple discrete and neutral delays, and the neutral delays are time varying, the stability is considered. Based on Lyapunov- Krasovskii functional method, a sufficient condition for asymptotical stability is established. The condition not only depends on the discrete delays but also on the neutral delays. And, a numerical example is presented to illustrate the effectiveness of the result, and some results are extended and improved.