Exponential stability of artificial neural networks with distributed delays and large impulses

This paper illustrates that there is a globally exponentially stable unique equilibrium state in an artificial neural network that is subject to delays distributed over unbounded intervals, and also to large impulses that are not too frequent. The activation functions, which may be unbounded, nondifferentiable and/or nonmonotonic, are assumed to be globally Lipschitz continuous. The stability analysis exploits the method of Lyapunov functions and the technique of Halanay inequalities to derive a family of easily verifiable sufficient conditions for convergence to the unique equilibrium state. The sufficiency conditions, in the norm either ∥·∥p∥·∥p where p⩾1p⩾1 or ∥·∥∞∥·∥∞, include those that govern the network parameters and the impulse magnitude and frequency.