Studies In The Control Method With Stochastic Jumping System’s

In this rapidly developing world,the requirement of any things are strict and accurate.However,there are many phenomena occur randomly in real life,so it is necessary to analyze from the perspective of random and thinking.In the stochastic systems,the research value of Ito stochastic system and the stochastic jump systems is immeasurable,the above two types of stochastic system is worthy of in-depth discussion and research topic.In this paper,the meaning and background of this paper for the related system has been narrated,and briefly describes the stochastic systems with Markov jump system development situation.Then introducing the problem of Brownian motion,Markov process,Ito integral and Ito formula,Lyapunov functional theory,stability theory and basic knowledge of matrix inequalities related in this paper.Contents of this paper as follows:Firstly,we study the general Lyapunov functional type solutions about complex the Ito-type solution of Ito type stochastic differential systems and random Markov jump system.Expression is similar the function of composite stochastic differential equations Ito type solution is given,this expression is called functional variation of Ito formula.The paper describes the whole theory is derived and proved to be rigorous and complete.Numerical examples illustrate the feasibility conclusions.Secondly,Ito stochastic systems are analyzed and studied,which is mainly for the stability and stabilization of the Ito stochastic differential system.On the basis of Ito stochastic differential equation systems of Ito formula,at the same time using Lyapunov functional stability theory and LMI-related knowledge,it is concluded that the stochastic stability and stochastic stabilization conditions.Meanwhile,the state feedback controller is designed.The last numerical examples illustrate the feasibility conclusions.Finally,on the basis of the Ito stochastic systems of studying,we analyzed the stochastic stability and stochastic stabilization of stochastic Markov jump system.Meanwhile,the state feedback controller is designed.Then numerical examples illustrate the feasibility conclusions.