Stable analysis for neural networks: Set-valued mapping method

By constructing some complete metric spaces, this paper investigates the stable problem for a class of neural networks. On the basis of set-valued mapping theory, by introducing the notion of essential equilibrium point, some sufficient and necessary criteria guaranteeing the existence and stability of the equilibrium point are established when the activation function and uncertain parameter vary continuously. Different from most of previous works on the stability problem of neural network, the feature of the method used in this paper does not depend on any Lyapunov functional.