Robust H_? Control And H_? Filtering For A Class Of Nonlinear Uncertain Stochastic Time-Varying Delayed Systems

There are various stochastic phenomena exist widely in practice systems,such as physical systems,technical systems and economic systems,the study of stochastic system has gained extensive attention.In recent years,the control problem of stochastic system has become a popular research topic.Since the foundation of Zames in control theory in 1981,H_? control has become one of the most popular research fields and a very important robust control method.When the model of the system is subject to the influence of external disturbance,the aim of H_? control is that,the designed controller can effectively restrain the disturbance to a given level.Compared with other types of control,H_? control is not necessary to know exactly the statistical properties of the external disturbance.It is only assumed that the energy of external disturbance is bounded.As a result,the research on H_? control has important theoretical and practical value.Using Lyapunov function and Lyapunov-Krasovskii functional,this paper researched stability,stabilization,H_? control and H_? filtering for a class of nonlinear uncertain stochastic time-varying delayed systems based on linear matrix inequalities(LMIs).The main work of this paper has the following aspects:Firstly,this paper studies the robust stochastically stability and stabilization for a class of nonlinear uncertain stochastic time-varying delayed systems.Specifically,the uncertain parameters considered are included both in system states and control and they are norm-bounded.A sufficient condition is presented for robust stochastically stability and stabilization of a class of nonlinear uncertain stochastic time-varying delayed systems in terms of LMIs.And a numerical example with simulation is provided to demonstrate the effectiveness of the proposed method.Secondly,this paper studies the robust H_? control for a class of nonlinear uncertain stochastic time-varying delayed systems.When the system is subjected to the influence of external disturbance,we design a robust H_? state-feedback controller,such that the system with admissible uncertainties and nonlinearities is not only robust stochastically stable but also robust H_? controllable.Then,a sufficient condition for the existence of the desired H_? controller is presented via LMIs.Finally,an example is given to demonstrate the effectiveness of the proposed method.Then,this paper researches the robust H_? filtering for a class of nonlinear uncertain stochastic time-varying delayed systems.When the state of a system is not available for direct measurement and hence have to be estimated in some ways.Compared with the well-known Kalman filtering approach,H_? filtering is not necessary to know exactly the statistical properties of the external disturbance.It is only assumed that the energy of external disturbance is bounded.In this paper,we design a full-order filter such that the dynamic filtering error system is exponentially mean square stable with admissible uncertainties and nonlinearities.Then,a sufficient condition is obtained for exponentially mean square stable of the dynamic filtering error system.Sufficient condition for the existence of desired H_? filter,which is given in terms of LMIs.And an illustrative numerical example is presented to demonstrate the effectiveness of the proposed method.Finally,the concluding remarks are summarized and some future works which may be further investigated are pointed out.