A Class Of Stochastic Nonlinear Varying Delay Systems With Memory Control,

The uncertainties and external disturbances are frequently encountered in many practical dynamic systems. These factors usually impact systems in a stochastic way. On the other hand, time delays are frequently found in many control systems, the existence of time delays is usually one of the main causes of instability and performance depravation for a system. As the performance requirements of the systems are becoming more and more higher, all these factors should be taken into consideration when analysing the system performances. Therefore, it is important to consider the stability and robust control problem for uncertain stochastic systems with time-delay.The existing literature seldom involves the research on memory state feedback control for stochastic nonlinear uncertain systems with time-varying delay. The problem is to design memory state feedback controllers such that the resulting closed-loop system is robust stochastic stable and satisfies a prescribed H_∞and guaranteed cost performance level. With applications of the theories and approaches of Lyapunov-Krasovskii function, Convex Optimization algorithm, Ito formula, Schur complement lemma, linear matrix inequality (LMI) in this thesis, we transform the control problems into a feasible issue of certain LMIs. Some delay-dependent 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 numerical examples to illustrate the effectiveness and availability for the proposed methods.