| Stochastic interference is common in nonlinear systems in real life,and stochastic nonlinear systems expressed by It? type calculus are the main forms to describe interference terms.In recent years,the research on stochastic nonlinear systems has received extensive attention and is one of the problems in nonlinear control theory.Because the stochastic nonlinear system can’t use the conventional Riemann integral calculation,it brings difficulties and challenges to the stability analysis of this kind of system.In addition,many practical stochastic nonlinear systems(such as robot systems,financial systems,etc.)need further study on the selection of Lyapunov functions for judging stability and how to design controllers to realize the stability of closed loop systems.Therefore,it is of great theoretical significance and application value to carry out the stability of stochastic nonlinear systems in this paper.In this paper,the problem of numbering of multiclass functions is studied,the stability analysis of It? typed stochastic nonlinear systems is carried out by using the research results,and the design method of stability controller for a It? type stochastic nonlinear system is discussed.The main work is as follows:1.In this paper,three nonlinear types of functions related to time variables and spatial variables are constructed,and through the study of their coefficients,a series of sufficient conditions for judging positive definite,negative definite and indefinite types of nonlinear functions are obtained.2.Based on the above study of the fixed number of functions,the stochastic asymptotic stability of the zero solution of the stochastic nonlinear system is studied,and the conditions for judging the stochastic asymptotic stability of the zero solution of the system are obtained by analyzing the coefficients of the It? type stochastic nonlinear system.3.This paper studies the design method of the controller when the zero solution of the It? type stochastic nonlinear system with zero input is not randomly asymptotically stable,discusses whether there is a linear controller,so that the zero solution of the system can be randomly asymptotically stable,and gives the solution method of the linear controller. |
