Asymptotic Stabilization In Probability And Almost Sure Exponential Stability Analysis Of Hybrid Stochastic System

Stochastic process is a mathematical model of time process affected by random factors.There exist random factors inevitably in the actual system,a lot of actual systems also can't avoid it's influence.Such that in many fields and engineering practice,stochastic system is widely used,the theory of stochastic system has also attracted many scholars' attention.One important class is the hybrid stochastic differential equations with Markov switching,also known as hybrid stochastic differential equations.This dissertation systematically studies the stability of general hybrid stochastic systems with Markov switching and random Cohen-Grossberg neural networks with Markov switching.Based mainly on switching stationary distribution,using Borel-Cantelli's lemma,Chebyshev's inequality and other random analysis techniques,a special Lyapunov function is constructed to obtain serial corollaries and theorems for the asymptotic stabilization in probability and almost sure exponential stabilization of the system.The dissertation is mainly made up of the following parts:1.An introduction to the background and significance of stochastic hybrid system and neural networks is given.Then,the preliminary knowledge is given.2.Based on the discrete time state observation,the almost sure exponential stabilization of a class of stochastic differential equations is studied.A feedback controller is added to both the diffusion term and the drift term,choosing the appropriate Lyapunov function and using the method of stable distribution and stability analysis of Markov chain,the stability condition of hybrid system is obtained,the feasibility of the results is demonstrated by the stability of the system with linear feedback controller.3.The probabilistic stability of a class of stochastic Cohen-Grossberg neural network with Markov switching is studied.Based on Lyapunov stability theory,the discriminant condition of stability based on the form of linear matrix inequality is obtained by using the properties of Markov switching and transfer probability.4.Focused on the problem of almost sure exponential stability analysis of a class of stochastic Cohen-Grossberg neural networks with Markov switching.First of all,using the concept of Markov stationary distribution,by constructing a special function,the low order moment exponential stability of free-delay Cohen-Grossberg neural networks is established.Then,the almost sure exponential stability of delay system is got through random analysis technique.Finally,the full text is summarized.