Modern control theory, which came into being in the 1950s, has been quickly developed, 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 dynamics 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 timedelay, which is frequently appeared in the systems, uncertain parameter disturbance and stochastic factor etc. That is stochastic robust HÃ¢Ë†Å¾control 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 HÃ¢Ë†Å¾control and filter design for neutral stochastic timedelay systems. For several different classes of neutral stochastic timedelay systems, in virtue of the approach of LyapunovKrasovskii functional, delay partition, free weighting matrices etc. timedelay methods, together with linear (nonlinear) matrix inequality technique, stochastic Markov jump bounded real lemma is obtained, and the stochastic dynamic output feedback controller, HÃ¢Ë†Å¾filter, nonfragile robust HÃ¢Ë†Å¾, controller, based on observer nonfragile robust HÃ¢Ë†Å¾controller, delay feedback HÃ¢Ë†Å¾controller 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 uncertainties satisfy admissible conditions, the stochastic stabilization problems are studied. Under the nonzero disturbance input, a fullorder stochastic dynamic output feedback controller is designed by solving a bilinear matrix inequality (BMI). At last a fullorder filter is designed for all admissible uncertainties and timevarying delay by similar approach, which is expressed in the form of linear matrix inequality (LMI).The conception of stochastic robust HÃ¢Ë†Å¾control for stochastic Markov jump systems is given, and the mathematical description of corresponding performance index is presented. Then, together with Doob martingale inequality, BorelCantelli 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 HÃ¢Ë†Å¾control problem for a class of stochastic system with Markov jump parameter is discussed, and the state feedback robust HÃ¢Ë†Å¾controller is designed.For a class of neutral stochastic delay system with Markov jump parameter, by employing a LyapunovKrasovskii functional, the delaydependent stochastic Markov jump bounded real lemma is presented at first. Then, nonfragile robust HÃ¢Ë†Å¾controller is designed by using the lemma, the controller gain are variable in additive form or multiplying form. The nonfragile observerbased stabilization and HÃ¢Ë†Å¾control problems for the neutral stochastic hybrid systems with timevarying delay are studied. The delaydependent sufficient conditions for the existence of the nonfragile HÃ¢Ë†Å¾controller and observer are given, which is nonfragile or resilient with respect to errors in the controller coefficients and observer coefficients. Under the control of the nonfragile observerbased HÃ¢Ë†Å¾controller, the resulting closedloop system not only is robust stochastic exponential stable in mean square but also satisfies the HÃ¢Ë†Å¾performance index.Dividing the delay interval into multiple segments, different weighting matrices in the new LyapunovKrasovskii functional are chosen. Based on the ideal of delay feedback, combining the stochastic integral inequality with nonlinear stochastic analysis, the delaydependent sufficient criteria of stabilization and robust HÃ¢Ë†Å¾control 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 HÃ¢Ë†Å¾and filter design for neutral stochastic delay systems in this dissertation not only enriches the stochastic robust HÃ¢Ë†Å¾control theory, but also extends the approach for stochastic robust HÃ¢Ë†Å¾control. Numerical examples illustrate the validity of the results and the effectiveness of the proposed methods.
