Stability And Control Problem Of Neutral Stochastic Markovian Jump Systems

The Markov jump system is a special kind of hybrid system that can describe the random mutation phenomenon well.It is widely used in various fields of modern industry,especially in the field of control science.At present,in order to solve the actual needs,more and more scientists are investing in the research of Markov jump systems,and have achieved remarkable results in the stability study of the system.This paper mainly studies stability and stabilization of a class of neutral Markove jump systems.The main structure of the paper is:Firstly,based on the definition of D operator stability,the paper finds the general conditions for making the neutral Markov jump system stable.By introducing the spectral radius condition,the conditional conservatism is reduced and a new condition is obtained.This new condition will be a basis for subsequent stability analysis,we finally found a new sufficient condition to make the system stable through a series of analyses.Further,The next content is about the proof of stability of Markov jump system.It mainly use Lyapunov-Krasovskii functional method to constructs appropriate Lyapunov-Krasovskii functionals,and then we uses the basic rules of Ito integral to construct the slack variable.These variables are established to satisfy the sufficient conditions of linear matrix inequality for the stability of neutral Markov jump systems.After that,we chose a simpler Lyapunov-Krasovskii functional,and used some inequality techniques to properly scale and obtain the new LMI conditions of the system.On this basis,we designed a feedback controller to study the stablization of the systems.Finally,three numerical examples are given in this paper,which verify the feasibility of the above conclusions and compare the superiority of the two stability conclusions given in the paper.