Stability Of Delayed Neural Networks

This dissertation mainly studies the stability of delayed neural networks and consists of three chapters.In chapter 1,section 1, The problem of asymptotic stability for a class of time-varying and time-delay system is studied. The method of decomposition for large-scale system and a generalized inequality are used in concluding the sufficient conditions for the system, and the estimate of the solution of differential equation under neural conditions is used in the discussing of the exponential stability of the solution for a neural system with time-delay. Above all, all the discussing is under the system with time-delay. Section 2 The problems of BIBO and robust stabilization for Systems with time-delay and Nonlinear Perturbations are discussed .First by using the method of Lyapunov function ,robust stabilization of the system is analyzed .Then,using Gronwall inequality ,the BIBO stabilization is analyzed. Two sufficient conditions for the systems are concluded from the research .All the researches are on the base of prior reference and the results of this paper is quite different and superior to the results of correlated reference.Section 3 Using the Dini derivative and integral inequality; the stability of delayed neural network is studied.Section 4 The case of stability of nonlinear delay neural network under the variable delay is studied, and we have the less conservative result. Chapter 2 Different to the stability of the 1 chapter, we studied the stability of —gain stability .We have known that though the system have Lyapnov stability it may be not have —gain stability. It is necessary to discuss the —gain stability. Chapter 3 we discuss the exponential stability of a new Hopfield neural network: BAM neural network.