Stabilization For Highly Nonlinear Stochastic Systems

This thesis is devoted to the research of the stabilization for stochastic systems under the highly nonlinear growth condition.This work is divided into two sections.In the first section,we investigates the following stochastic coupled systems satisfying highly nonlnear growth condition:#12#12 where xi(s)=(xi(1)(s),xi(2)(s),…,xi(m)(s))T is the state vector at the time s,fi,gi:Rm ×R+?Rm are continuous functions,the differentiable function aih(s)stands for coupling strength.The function Hih indicates the influence from vertex i to vertex h.Concentrating on the finite-time stability,we borrow Kirchhoff's Matrix Tree Theorem and highly nonlinear correlation theorem to achieve stabilization.In section 2,we consider the issue of stabilization of a class of stochastic systems with Markov switching and high nonlinear coefficient conditions.To be specific,for a unstable hybrid stochastic system under highly nonlinear growth conditions dZ(s)=q(Z(s),r(s),s)ds+p(Z(s),r(s),s)dB(s),s?0.(2)Our goal is to design a controller U(Z(s),r(s),s)operates in the drift term to stabilize the systems dZ(s)=[q(Z(s),r(s),s)+U(Z(s),r(s),s)]ds+p(Z(s),r(s),s)dB(s),s?0.(3)The controller U(Z(s),r(s),s)operates on the discrete time states,which takes the following form#12 where Z(s)=(Z1(s),Z2(s),…,Zm(s))T describes the state vector at the time s,q,p:Rm×S×R+?Rm,with the initial value Z(0)=Z0,?(s)=[s/?]?,? is the time interval between two consecutive observations,T is the control period,? is the working time width of the control with 0<?<T.This paper mainly compares the controlled stochastic hybrid system with high nonlinear coefficient condition and periodically intermittent based on discrete observations with the controlled stochastic hybrid system with periodically continuous drift,rather than Lyapunov functional method.This is different from the general way to deal with the stability of hybrid stochastic system.