Study On The State Estimation And Invariant Set Of Neural Networks With Impulsive And Stochastic Disturbance

Based on appropriate Lyapunov functions stochastic analysis technique and someinequality techniques, four classes of neural networks with time-varying delays arediscussed. They are impulsive CGNNs with time-varying delays, impulsive neuralnetworks with time-varying delays, stochastic CGNNs with time-varying delays andstochastic BAM neural networks with time-varying delays and infinite distributed delays,mainly research the invariant set, passivity and convergence of these systems. The paper isdivided into six chapters. Main contents are as following:In Chapter1, we introduce the research status for impulsive neural networks,stochastic neural networks, state estimation and invariant set of neural networks.In Chapter2, we give a new definite of Lagrange stability and establish a class of newdelay impulsive differential inequality. By constructing suitable Lyapunov functions, wemainly research the Lagrange global exponential stability of a class of impulsive CGNNswith time-varying delays. Meanwhile, the estimations of the global exponential convergentball are given out.In Chapter3, we mainly analysis the passivity of a class of impulsive neural networkswith time-varying delays. By choosing appropriate inequality and constructing suitableLyapunov-Krasovskii functionals, some sufficient conditions for passivity of the impulsiveneural networks are given.In Chapter4, we give a novel delay operator differential inequality and investigate theLagrange global exponential p-stability of a class of stochastic CGNNs with time-varyingdelays. To this end, by constructing suitable Lyapunov functions and combining withstochastic analysis technique, we establish some new sufficient conditions for the Lagrangeglobal exponential p-stability of the considered system.In Chapter5, we give a novel delay operator differential-integral inequality anddiscuss the global exponential convergence of a class of stochastic BAM neural networkswith time-varying delays and infinite distributed delays. Some sufficient conditions forexponential convergence of the neural networks are given.In Chapter6, we summarize the whole text and point out the prospect, mainly give atotal conclusion of the research work of this thesis. Meanwhile, we put forward some ideaswhich need to be further discussed.