Robust Control And Filter For Continuous Stochastic Time-delay Systems

Since stochastic systems have come to play an important role in many branches ofscience and engineering applications, stochastic systems have been widely investigated inrecent years. The dissertation provides some results and concepts on robust H_∞controlfor uncertain stochastic time-delay systems, robust control for the uncertain stochastictime-delay markovian jump systems, and filtering for the uncertain singular stochastictime-delay systems. The main results obtained in this dissertation are as follows:1,The problems of robust stochastic stabilization and robust H_∞control forstochastic systems with parameter uncertainties and state delays are addressed,respectively. The parameter uncertainties are of the polytopic form and linear fractionalform, respectively. Attention is focused on the design of state feedback controllers. Forthe robust stabilization problem, a state feedback controller is designed such that theclosed-loop system is robustly stable in mean square, while for the robust H_∞controlproblem, a state feedback controller is designed such that the closed-loop system is notonly robustly stable in mean square but also with a prescribed H_∞performance level.2,The problem of the L₂-L_∞filter design for a class of stochastic time-delaysystems is concerned. By the introductions of slack varialbles, delay-dependent sufficientconditions are presented, which guarantee the existence of a linear filter ensuring that thefiltering error system is stochastically stable in mean square and its L₂-L_∞performance satisfies a prescribed level. A desired filter can be constructed by solvingcertain linear matrix inequalities. A simulation example is given to demonstrate the lessconservatism of the proposed method.3,Based on the results in the first part, we consider the problems of robustexponential stabilization in mean square and robust H_∞control for time-delaystochastic systems with Markov jump parameters and parameter uncertainties. Attentionis focused on the design of state feedback controllers, which ensure the closed-loopsystem is not only robustly exponential stable in mean square but also satisfies aprescribed H_∞performance level.4,The robust H_∞filtering problem for a class of uncertain singular stochasticsystems with time-delay and uncertain singular stochastic Markovian jump systems are studied based on the extended Ito stochastic differential formula. By means of thesingular stochastic Lyapunov method and linear matrix inequalities(LMIs),delay-dependent sufficient conditions and delay-independent sufficient conditions areobtained, respectively, such that the filtering error system is robustly stable in meansquare with a prescribed disturbance attenuation level.