State Feedback Stabilization For A Class Of High-order Stochastic Nonlinear Systems

In recent years,researchers have conducted many discussions on the stability theory of stochastic system.In some respect,it has achieved fruitful theoretical results,such as controller design and theoretical analysis.The time-delay system has a rich theoretical foundation and background.However,many control systems often have poorer performance due to the presence of random time lags.Therefore,the study of random time-lag in control systems has attracted wide attention from both scholars in both principle and planning practice.This paper focuses on a class of high-order stochastic nonlinear systems with time delays.The main theories used in this paper are Lyapunov stability theory,LyapunovKrasovskii theory of stochastic systems and back-stepping design methods.Finally,w e designed a suitable state feedback controller for the system.The main content of this article includes:Firstly,for the problem of multi-state systems,the problem of state feedback stab ilization for a class of higher-order stochastic nonlinear systems is studied.Using the stability theory of stochastic systems and combining the back-stepping design method and selecting the appropriate Lyapunov function to a state feedback controller is designed for the system so that the balance point of the closed-loop system is globally asymptotically stable.Finally,the simulation results show that the control scheme is effective.Secondly,we have expanded the stochastic system.studied at the state feedback co ntrol problem for stochastic time-varying nonlinear systems with time-varying delays.Constructing the state feedback controller makes the balance point of the closed-loop s ystem globally asymptotically stable by construct a proper Lyapunov function combine d with a back-stepping design method and also use inequality transformation technique s to handle nonlinear terms in the derivative.Eventually,the simulation results show t hat the control scheme is effective.Thirdly,development of the issue of multiple system by using states Lyapunov Kresovskii general theory and backstepping design method by referring to a stochastic system.On the basis of Chapter 2,we investigate the state feedbackstabilization problemfor a class of high order stochastic time-varying delay systems.The state feedback controller it constructs makes the closed-loop system globally asym ptotically stable at the equilibrium point.Finally,ultimately,the simulation results show that the control scheme is effective.