Analysis And Design Of The Reduced Order Filtering For Stochastic Time Delay System

The inputs and measurement outputs of stochastic systems are often affected by stochas-tic noises, which will lead to poor performance and even instability. Stochastic systems are more complex than deterministic ones, since for the formers it is necessary to consider the sta-tistical properties. The study of stochastic systems is of theoretical importance. On the other hand, time delays are frequently encountered in the process of signal transmission, and systems with delays have been investigated widely in the past years. In contrast with full-order filters, reduced-order filters are simpler and easier to be implemented. Based on the above-mentioned considerations, this thesis the problem of full-order filtering for stochastic systems with time delays is investigated.First, the H_? reduced-order filtering problem for a class of stochastic time-delay systems is studied. The filtering error system is constructed, and H_? performance analysis result is proposed. Then an H_? reduced-order filter stochastic time-delay systems is design in terms of linear matrix inequalities ?LMIs?.Second, it concerns with finite time H_? reduced order filtering for stochastic time-delay systems. By adopting a reduced order filter, the filtering error system is obtained. Based on Lyapunov theory, finite time H_? performance analysis result of the filtering error system in sense of mean square is presented, and then the filter parameters are constructed.Third, finite time L₂ - L_? reduced order filtering for stochastic time-delay systems with nonlinearities is investigated. The existence of the filter is presented by means of a set of LMIs. The filtering error system is mean square finite time stable with given L₂ - L_? performance under the designed filter.Finally, the contents of this thesis are summarized briefly, and the future works are pro-posed.