Stability And Stabilization Of Markov Jump Stochastic Systems With Unknown Transition Rate

Neutral stochastic time-delay Markov jump systems(NSDMJSs)are widely used in practical engineering control systems.However,in practical control systems,it is difficult to measure all the information of the transiton rate,and some measurements have certain errors.Therefore,when modeling the control system,we must consider these unknown information and the error of the information.This paper is to study a kind of NSDMJSs mathematical model which is more suitable for the actual situation when the transiton rate is partially unknown.This paper mainly studies the following contents:Firstly,based on Lyapunov stability theory,the stability of NSDMJS with double time-delay and uncertain transition rate are studied.On the premise of ensuring the stability of D operators of neutral stochastic differential systems,then choosing a suitable Lyapunov-Krasovskii functional(LKF),combined with some inequalities,It(?)lemma,etc.The sufficient criteria of system stability are established in the form of linear matrix inequalities(LMIs).Secondly,the stabilization of the system is studied.Firstly,the relatively concise LKF is reconstructed,and the delay independent stability condition is obtained.On this basis,the same LKF is selected,and the feedback controller is designed,so that the parameters of the feedback controller are related to the present state,the past state and the neutral term,and then the control gain matrix is obtained to determine the stability of the NSDMJS closed-loop system.Then,the robust stability and stabilization of the system are studied.By using the inequality technique,the robust exponential stability condition of the system is obtained.On this basis,the controller is designed to study the robust stabilization of the system.Finally,four examples are given to verify the two stability theories respectively,and to design the feedback controller to ensure the stability of the closed-loop system,and then to verify the robust stability theory of the system.