Robust H_∞ Control And Filter Design For Neutral Stochastic Time-delay Systems

Modern control theory, which came into being in the 1950s, has been quickly devel-oped, and has been successfully applied in all kinds of engineering area. But, it has subjected to plenty of difficulty in the modern industrial applications. The main reason is that the dy-namics character is difficult to describe by the accurate mathematics model for the plenty of control objects. Even sometimes the precise mathematics model can be obtained, but the given model is so complex that we have to simplify the systems for effective analysis and synthesis. However, the accurate model is the research object in optimal control theory and modern control theory. So, it is difficult to satisfy the expected performance index for the controller, which is analyzed and synthesized for the reduced systems. Therefore, in the system modeling, we have to consider the effectiveness of time-delay, which is frequently appeared in the systems, uncertain parameter disturbance and stochastic factor etc. That is stochastic robust H∞control theory, which is to design corresponding controller such that the systems are inner stochastic stable and satisfy expected performance index.The dissertation focuses on the investigation of the robust H∞control and filter design for neutral stochastic time-delay systems. For several different classes of neutral stochas-tic time-delay systems, in virtue of the approach of Lyapunov-Krasovskii functional, delay partition, free weighting matrices etc. time-delay methods, together with linear (nonlinear) matrix inequality technique, stochastic Markov jump bounded real lemma is obtained, and the stochastic dynamic output feedback controller, H∞filter, non-fragile robust H∞, con-troller, based on observer non-fragile robust H∞controller, delay feedback H∞controller are designed respectively. Some results are also presented. The main research work and contribution of this thesis are listed as follows:Through constructing a Lyapunov functional, without the disturbance input and the un-certainties satisfy admissible conditions, the stochastic stabilization problems are studied. Under the nonzero disturbance input, a full-order stochastic dynamic output feedback con-troller is designed by solving a bilinear matrix inequality (BMI). At last a full-order filter is designed for all admissible uncertainties and time-varying delay by similar approach, which is expressed in the form of linear matrix inequality (LMI).The conception of stochastic robust H∞control for stochastic Markov jump systems is given, and the mathematical description of corresponding performance index is presented. Then, together with Doob martingale inequality, Borel-Cantelli lemma, stochastic integral inequality, ergodic theory of Markov chain, the stochastic Markov jump bounded real lemma is presented. Combing the lemma with linear matrix inequality technique, the robust H∞control problem for a class of stochastic system with Markov jump parameter is discussed, and the state feedback robust H∞controller is designed.For a class of neutral stochastic delay system with Markov jump parameter, by em-ploying a Lyapunov-Krasovskii functional, the delay-dependent stochastic Markov jump bounded real lemma is presented at first. Then, non-fragile robust H∞controller is de-signed by using the lemma, the controller gain are variable in additive form or multiplying form. The non-fragile observer-based stabilization and H∞control problems for the neutral stochastic hybrid systems with time-varying delay are studied. The delay-dependent suffi-cient conditions for the existence of the non-fragile H∞controller and observer are given, which is non-fragile or resilient with respect to errors in the controller coefficients and ob-server coefficients. Under the control of the non-fragile observer-based H∞controller, the resulting closed-loop system not only is robust stochastic exponential stable in mean square but also satisfies the H∞performance index.Dividing the delay interval into multiple segments, different weighting matrices in the new Lyapunov-Krasovskii functional are chosen. Based on the ideal of delay feedback, combining the stochastic integral inequality with nonlinear stochastic analysis, the delay-dependent sufficient criteria of stabilization and robust H∞control problems for a class of neutral nonlinear stochastic delay system are discussed in term of linear matrix inequality form. In the derivative process, neither model transformations nor boundedness techniques for cross terms are employed, which possibly produced the conservatism. A appropriate free weight matrix is also introduced, which reduced the conservatism of the controller and the complexity of the algorithm.Finally, the concluding remarks are summarized, and the future works which may be further investigated are presented. Overall, the study on robust H∞and filter design for neutral stochastic delay systems in this dissertation not only enriches the stochastic robust H∞control theory, but also extends the approach for stochastic robust H∞control. Numerical examples illustrate the validity of the results and the effectiveness of the proposed methods.