Robust Control And Filtering For Uncertain Discrete-Time Stochastic Systems With Distributed Delay

The stochastic systems are extremely common in industrial control areas such as, satellite attitude control, missile guidance control, and it also generally used in many domains, for example, transportation engineering, metallurgy, finance, and biotechnology. Moreover, the distributed delays widely exist in these fields such as, space flight, network control and signal communication. At present, the research regarding the stochastic systems with distributed delay is not fully studied, and there are still many open problems need to be further solved. Therefore, the research on the stochastic systems with distributed delay is theoretically significant.This thesis is concerned with the problems of robust stability and robust stabilization, robust H_∞control and robust H_∞filtering for a class of uncertain discrete-time stochastic systems with distributed delay, and the uncertainties are assumed to be norm-bounded. Incorporated and applied some latest developed methods and results on the robust control of discrete-time systems, delay systems and stochastic systems, some new results on the robust stability, robust control and robust filtering problems are proposed in this thesis. The results of the re-search are obtained by making fully use of the free-weighting matrix techniques and the linear matrix inequality approach. The detailed contents can be summa-rized as follows:1) The problems of robust stability and robust stabilization are considered for the class of norm-bounded parameter uncertainty of discrete-time stochastic systems with distributed delay. First, a delay-dependent sufficient condition, is proposed, which guarantees the system to be robustly mean-square asymptotic stable. To reduce the conservativeness of the proposed condition, the free-weighting matrix technique is applied. In addition, the linear matrix inequa-lity approach is used to formulate the sufficient condition, and it could be easily test by using some available softwares, such as LMI Tool-box in Matlab. More-over, the robust stabilization controller is designed, which assures the close-loop system to be robustly mean-square asymptotic stable.2) The problem of robust H_∞control for such a system is considered. First, a delay-dependent sufficient condition which ensures the nominal system to be mean-square asymptotic stable and has a prescribed H_∞performance level, is proposed in terms of linear matrix inequality. By making use of the free-weighting matrix techniques and the linear matrix inequality approach, the results obtained could be less conservative and easy to be test. Then, the H_∞ controller for the nominal system is designed such that the close-loop system is mean-square asymptotic stable and have a prescribed H_∞performance level. In addition, the above results are extended to the uncertain system case, and the re-lated results are also given.3) The problem of robust H_∞filtering is investigated for the class of sys-tems. First, a delay-dependent bounded real lemma is proposed in terms of linear matrix inequality, which guarantees the nominal system to be mean-square asymptotic stable and has a prescribed H_∞performance level. Then, the H_∞filter is designed, and the solvability condition for the filter parameters is also pro-posed. Finally, the related results on the filtering for the nominal system are ex-tended to the uncertain system case.In this thesis, all the main results on the class of uncertain discrete-time stochastic systems are given by the form of linear matrix inequality. By LMI Tool-Box in Matlab, the problems can be easily solved with a series of feasible solutions, not just one solution, and any of them can satisfy the conditions. In the end of every chapter, some numerical examples are provided to illustrate the ef-fectiveness of the proposed design scheme.