A Study Of Stability Of Variable-time Impulsive Systems And An Analysis Of Stability And Synchronization Of Neural Networks

Impulsive differential systems,stochastic differential systems and neural networks are also the hot topic of nonlinear systems.This thesis focuses on the stability of impulsive systems with time window and stochastic impulsive systems with variable-time impulses.The theories of impulsive differential system are used to discuss the stability and synchronization prob-lem of neural networks.The main contributions and originalities in this thesis are listed as follows:(1)The stability of impulsive systems with time window is studied.Firstly,comparison systems of impulsive differential systems with impulse time windows are established.Then two theorems are obtained to determine the different impulsive time windows for stable and unstable continuous dynamical systems,respectively.The effectiveness of the theoretical results are illustrated by two numerical examples.(2)The stability of stochastic impulsive systems with variable-time impulses is investigated via comparison method.We consider the case that the trajectory of the stochastic system intersects each surface of discontinuity exactly once.Then we shall show that under the well-selected conditions the variable-time impulsive systems can be reduced to the fixed-time impulsive systems with impulse time window.By using comparison method,we obtain two theorems to determine the different impulsive time windows for stable and unstable stochastic dynamical systems,respectively.The effectiveness of the theoretical results are illustrated by two numerical examples.(3)The global asymptotic stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays and reaction-diffusion terms is investigated.Under some suitable assumptions and using Lyapunow-Krasovskii functional method,we apply the linear matrix inequality technique to propose some new sufficient conditions for the global asymptotic stability of the addressed model in the stochastic sense.The mixed time delays comprise both the time-varying and continuously distributed delays.The effectiveness of the theoretical result is illustrated by a numerical example.(4)The problem of the impulse effects on the finite-time stability of neural networks with time-varying delay is investigated.Several novel conditions which guarantee the considered model is finite-time stable are obtained by the idea of Lyapunov-Krasovskii functional and average impulse interval.Moreover,the proposed sufficient condition can be simplified into the form of linear matrix equalities which can be easily solved by Matlab LMI toolbox.The obtained results show that the model can become finite-time stable with stabilizing impulse effects on one hand,and it can preserve the finite-time stability property in presence of destabilizing impulses on the other hand.Numerical examples are given to show the effectiveness of the obtained results.(5)The synchronization analysis for discrete-time coupled neural networks is investigated.The networks under consideration are subject to impulsive disturbances,time delays and the jumping parameters which are modeled as a continuous-time,discrete-state Markov process.Time delays include both the mode-dependent discrete and distributed delay.By constructing suitable Lyapunov-Krasovskii functional and combining with linear matrix inequality approach,several novel criteria are derived for verifying the global exponential synchronization in the mean square of such stochastic dynamical networks.The derived conditions are established in terms of linear matrix inequalities,which can be easily solved by some available software packages.Two simulation examples are presented to show the effectiveness and applicability of the obtained results.