State-feedback Stabilization Of Stochastic Time-delay Nonlinear Systems

As modern society increasingly information and systematization,more and more complexsystem appears in engineering technology, social economy, the ecological environment and soon. Therefore the disadvantages of control ductility are more prominent.So, for the controlproblem of time-delay systems,we faced a great challenge no matter in theory or inengineering practice,It is necessary for time-delay systems in-depth comprehensiveperformance analysis and control.Therefore, the research in the stability of the uncertain time-delay stochastic systems androbust control problems will have important theory value and practical significance.Based on stochastic time-delay systems and Lyapunov stability theory on back-steppingdesign method and the adding of a power integrator technique,we discussed the randomtime-varying time-delay state feedback stabilization problem for a class of nonlinearsystems.The main content of this paper include:1.By using the method of Lyapunov stability,we study the stability problem and outputfeedback controller of random time-varying time-delay nonlinear systems.2.The Razumikhin-type approach is introduced to solve the state feedback stabilizationproblem for a class of stochastic nonlinear systems with time-varying delay in our paper.Based on the Razumikhin-Mao theorem on stochastic systems and back-stepping designmethod, a state feedback controller is constructed to ensure the origin of closed-loop system isglobally asymptotically stable in probability.3.This paper studies the problem of state feedback stabilization for a class of stochastictime-varying delay nonlinear systems which are neither necessarily feedback linearizable noraffine in the control input. Based on the back-stepping design method and the adding of apower integrator technique, a state feedback controller is constructed to ensure the origin ofclosed-loop system is globally asymptotically stable in probability. The main design difficultyis how to deal with the different power orders which is not equal, time-varying delay. Theefficiency of the state feedback controller is demonstrated by a simulation example.