Exponential stability in Hopfield-type neural networks with impulses

This paper demonstrates that there is an exponentially stable unique equilibrium state in a Hopfield-type neural network that is subject to quite large impulses that are not too frequent. The activation functions are assumed to be globally Lipschitz continuous and unbounded. The analysis exploits an homeomorphic mapping and an appropriate Lyapunov function, and also either a geometric–arithmetic mean inequality or a Young inequality, to derive a family of easily verifiable sufficient conditions for convergence to the unique globally stable equilibrium state. These sufficiency conditions, in the norm ∥·∥p where p ⩾ 1, include those governing the network parameters and the impulse magnitude and frequency.