Stability And Stabilization Of Discrete Time/Nonlinear Stochastic Systems

Stochastic systems can simulate many practical systems,such as chemical reaction processes,mathematical finance,game theory models,etc.Therefore,the study of stochastic systems has attracted extensive attention from many scholars.On the other hand,as an important part of system theory,stability theory plays a very important role in practical engineering applications.This paper mainly studies the strong stability of stochastic system,which is divided into the following parts:(1)Mean-square strong stability and stabilization of discrete time stochastic systems with multiple multiplicative noises.The mean-square strong stability and strong stabilization of discrete stochastic systems with multiplicative noise are studied.Firstly,the definition of mean-square strong stability is given,and two necessary and sufficient conditions of mean-square strong stability are obtained,as well as the relation between mean-square stability and mean-square strong stability.Secondly,the sufficient and necessary conditions of state feedback and output feedback mean-square stabilization are obtained respectively,and the analytical expressions of state feedback controller and static output feedback controller are given respectively.Finally,the relation between static output feedback control and dynamic output feedback control under mean square strong stabilization is studied,and the equivalent condition of static output feedback controller design and dynamic output feedback controller design under mean square strong stabilization are obtained.(2)Strong stability and stabilization of discrete time stochastic Markov jump systems with multiple multiplicative noises.The strong stability and stabilization of discrete stochastic Markov jump systems with multiplicative noise are studied.Firstly,the definition of strong stability of discrete time Markov jump system with multiplicative noise is given,and the sufficient and necessary conditions of strong stability are obtained.Secondly The problem of strong stabilization under state feedback control is studied,and the sufficient and necessary conditions of strong stabilization under state feedback control are obtained,and the analytical expression of state feedback controller is given.Finally,the problem of strong stabilization under output feedback control is studied,and the sufficient and necessary conditions of strong stabilization under output feedback control are obtained.Meanwhile,the analytical expression of static output feedback controller is given.And on this basis,the relation between the dynamic output feedback controller and the static output feedback controller is obtained.(3)Stability and Stabilization of Nonlinear Stochastic Systems in Finite Time Loop Domain Based on Neural Network.Firstly,the definition of the stability of uncertain nonlinear stochastic systems in finite time loop domain is given.Secondly,the nonlinear term is approximated according to the multi-layer feedback neural network,and a sufficient condition for the system to be stable in the finite time loop domain is obtained.Thirdly,a state feedback finite time loop controller is designed,a sufficient condition expressed by matrix inequality is obtained,and the corresponding solution algorithm is given.Finally,an example is given to illustrate the validity of the above results.