H_? Control And Filtering For General Delayed Nonlinear Stochastic Systems With Markov Jumps

The H? control and filtering problems have attracted more and more attentions,because in practical applications the exact statistics information of exogenous disturbance can not be obtained some time. This thesis is concerned with the robust H? control and filtering problems of a class of general delayed nonlinear stochastic systems with Markov jumps, where time delay exists in state equation, measurement equation and controlled output.Firstly, H? control problem is studied. By using methods of completing the square, magnifying and reducing to solve a set of constrained Hamilton-Jacobi inequalities, the infinite horizon exponential mean square H? controller design is presented, and then the globally asymptotic stable one. Then the finite horizon H?controller of the systems is presented in the similar way and the difference between it and the result of the infinite horizon case is analyzed.Secondly.H? filtering problem is researched. A filtering equation, more general than the Luenberger-type one, is constructed and then by the similar way in H?control problem, a nonlinear stochastic bounded real lemma for nonlinear delayed Markov jump systems is introduced. Dealing with the augmented system via the nonlinear stochastic bounded real lemma, the exponential mean square H? filter is presented. And then the asymptotic mean square H? filter design is obtained.Finally. considering that the coupled Hamilton-Jacobi inequalities in the results obtained before are hard to solve, the global linearization approach is introduced based on the T-S fuzzy model. By designing the fuzzy rules and applying the fuzzy blending method, the research object is transformed from the nonlinear system to linear one, to which the results obtained before are applied. Via matrix operations such as Schur's complement, the results of H? control and filtering problems are turned into solving a set of linear matrix inequalities respectively.Meanwhile, the corresponding numerical examples are given to show the effectiveness of our results.