A note on the global stability of dynamical neural networks

It is shown that the additive diagonal stability condition on the interconnection matrix of a neural network, together with the assumption that the activation functions are nondecreasing, guarantees the uniqueness of the equilibrium point. This condition, under the same assumption on the activation functions, is also shown to imply the local attractivity and local asymptotic stability of the equilibrium point, thus ensuring the global asymptotic stability (GAS) of the equilibrium point. The result obtained generalizes the previous results derived in the literature.