Exponential stability of delayed stochastic cellular neural networks

In view of the character of saturation linearity of output functions of neurons of the cellular neural networks, the method decomposing the state space to sub-regions is adopted to study almost sure exponential stability on delayed cellular neural networks which are in the noised environment. When perturbed terms in the model of the neural network satisfy Lipschitz condition, some algebraic criteria are obtained. The results obtained in this paper show that if an equilibrium of the neural network is the interior point of a sub-region, and an appropriate matrix related to this equilibrium has some stable degree to stabilize the perturbation, then the equilibrium of the delayed cellular neural network can still remain the property of exponential stability. All results in the paper is only to compute eigenvalues of matrices.