Time Delay Dependent Passivity Analysis For Time-varying Delay Neural Networks

Neural networks(NNS)have been successfully used in a great deal of fields,for example,signal processing,pattern recognition,associative memory control and other areas.Therefore,to study the stability of neural network system is very important because it not only has research value but also has great practical meaning.In reality,time delay systems are present to in neural networks day to day,some of which are sources of instability and oscillation from time to time.This paper studies the passivity problem with time-varying delay stochastically perturbed neural network system.On account of the theory of functional differential equations and neural network,two kinds of neural network systems are discussed.The following research results are obtained:Firstly,the passivity of impulsive neural networks with time-varying delays and random perturbations is discussed.By using the relevant definitions and lemmas,we construct the brand new Lyapunov-krasovskii functional,and apply the method of matrix inequality skillfully,some new delay-dependent passivity conditions are proposed in terms of the full use of the conditions of neuron activation functions and involved time-varying delays.These passivity conditions are presented in accordance with matrix inequalities,which can be easily verified via standard numerical software.Meanwhile,the results derived here include the existing relative results on the passivity for neural networks without impulse effects as special cases.The results can also be extended to other more complex neural networks with impulsive interference.Secondly,we deal with the problems of with time-varying delay stochastically perturbed neural network system,By combining the relevant definitions and lemmas,we construct the new Lyapunov-krasovskii functional,and apply the method of matrix inequality.In this paper,the conditions of exponential passivity of stochastic neural networks with uncertainties and time-varying delays are given.The results are extended to two types of uncertainty: time-varying parameter uncertainty and uncertainty of the Markov switching type,get the passivity condition index is established,and specifically what I mean that the exponential passivity of Markovian switching stochastic neural networks contains a non Markovian switching neural network as a special case.Finally,The feasibility of the final result can be tested by twonumerical examples.