Research On Stability And Synchronization Control Of Recurrent Neural Networks With Time Delays

Neural networks are mathematical models to simulate behavior mechanisms of the brain and perform information processing.Neural networks are composed of many neurons connected by synapses,which have the capacities of self-adapting,self-organization,and self-learning.In recent years,neural networks have been extensively utilized in associative memories,signal processing,combinatorial optimization,pattern recognition and secure communication.It should be pointed out that those practical implementations are dramatically associated with dynamical properties of neural networks.For instance,when a neural network is used to solve combinatorial optimization problems,it is generally required to own a unique and globally stable equilibrium point preventing the neural network from the risk of getting trapped in some local minimum of the energy function.Hence,dynamical analysis of neural networks becomes a research topic in academia.In the process of theoretical analysis for neural networks,time-varying delays,uncertainties,stochastic noise and diffusion phenomena particularly affect the properties of neural networks.During the last three decades,great efforts have been dedicated to study global stability of neural networks under the effect of those factors,and a large number of outcomes have been published.Yet,for recurrent neural networks with time delays,it should be extensively investigated that how to obtain global exponential stability criteria with a lower conservatism by using linear matrix inequalities.When unbounded time delays and diffusion phenomena are both incorporated into neural networks,how to analyze the stability and synchronization is a problem.Besides,for stochastic delayed reaction diffusion neural networks,how to design an impulsive controller to realize exponential synchronization.In view of those problems,based upon the published results,we attempt to carry out the research.The main results of this dissertation are as follows.Global exponential stability of recurrent neural networks with time delays is investigated.First,we give a lemma to analyze stability.By using this lemma,some global asymptotical stability criteria can be reinforced to global exponential stability ones.Then,through dynamical partition the delay interval,furthermore,by constructing Lyapunov-Krasovskii functionals,and utilizing the reciprocally convex combination approach and Wirtinger-based integral inequality,delay-dependent global exponential stability criteria are derived in terms of linear matrix inequalities.Synchronization of reaction-diffusion neural networks with Dirichlet boundary conditions and infinite discrete time-varying delays is analyzed.By utilizing theories of partial differential equations,Green's formula,inequality techniques,and the approach of comparison,algebraic criteria are presented to guarantee master-slave synchronization of the underlying reaction-diffusion neural networks via a designed state feedback controller.Additionally,we discuss exponential synchronization of reaction-diffusion neural networks with finite time-varying delays.The global ?-type stability and robust stability of stochastic reaction-diffusion neural networks with Dirichlet boundary conditions,infinite discrete time-varying delays,and infinite continuously distributed delays are considered.By virtue of inequality techniques,properties of M-matrix,and theories of stochastic analysis,several sufficient criteria are obtained to guarantee the almost sure ?-type stability,pth moment ?-type stability,and ?-type robust stability of the underlying stochastic reaction-diffusion neural networks with hybrid unbounded time delays.With appropriate choices of the function ?,the ?-type stability reduces to the exponential stability,polynomial stability,and logarithmic stability.Impulsive synchronization of stochastic reaction diffusion neural networks with Dirichlet boundary conditions and hybrid time-varying delays is concerned.By exploiting inequality techniques,theories of stochastic analysis,linear matrix inequalities,and the contradiction method,sufficient criteria are proposed to ensure exponential synchronization of the addressed stochastic reaction diffusion neural networks with mixed time delays via a designed impulsive controller.Finally,conclusions in the dissertation are collected,and future works are proposed.