Nonlinear Stochastic Delay System Stability And Control Problems

Nonlinear control system inevitably encounter uncertainties and external disturbances. These uncertainties and disturbances usually impact systems in a stochastic way. Based on this point, it is necessary to adopt a stochastic model to describe an engineering dynamic system. On the other hand, time delays are frequently found in many control systems. The existence of time delay is usually one of the main causes of instability and worse performance for a system. Therefore, it is quite important to investigate the stability and the control of delay nonlinear stochastic system in theoretical and engineering sense.Uncertain stochastic systems are considered with the coefficient of the stochastic variable in the form of nonlinear function in this thesis. We mainly focus on the problems of state feedback robust control in the following aspects: The exponential stability in mean square; The locally exponential stability in mean square; Guaranteed cost control; H_∞guaranteed cost control. With applications of the theories and approaches of Lyapunov stability, Ito formula, Schur complement lemma, Linear matrix inequality(LMI), we transform the control problems into a feasible issue of certain LMIs. Some sufficient conditions for the solvability of the problems are obtained. The expressions of the desired controller are given. Via the MATLAB LMI control toolbox, we provide simulation examples to illustrate the application and effectiveness of the proposed methods.