Stochastic Differential Delay Systems, Robust H_ ¡Þ

Since stochastic systems have come to play an important role in many branches of science and engineering applications, stochastic systems have been widely investigated in recent years. This paper provides some results and concepts on H∞control for stochastic time-delay systems, and filtering for the linear stochastic time-delay systems. The main results obtained in this dissertation are as follows:1)In chapter 1, we study the H∞filtering design for a class of stochastic systems with time delay Based on the Ito stochastic differential formula and LMIs, delay-dependent sufficient condi-tions are presented, which guarantee the existence of a filter ensuring that the filtering error system is robustly asymptotically stable in the mean square and its H∞performance satis-fies a prescribed level. A desired filter can be constructed by solving certain linear matrix inequalities. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.2)In chapter 2, we consider the problem of robust H∞guaranteed cost control for stochas-tic systems with parameter uncertainties and time-varying delays The parameter uncertainties are of the linear fractional form. State-feedback controller is presented based on Lyapunov functional approach. The designed controller ensures that the closed-loop system is robustly stochastically exponentially stable in the mean square and with a prescribed H∞disturbance attenuation level. The cost function value is not more than a specified upper bound for all admissible uncertainties. Sufficient conditions for the existence of the designed controller are presented in terms of linear matrix inequalities(LMIs). Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.