Asymptotic stability of equilibrium points in dynamical neural networks

Abstract

In most applications of feedback neural networks, such as the realisation of associative memories, the asymptotic stability of specific equilibrium points is the main design requirement. Sufficient conditions are presented which simplify the checking that an isolated equilibrium point is asymptotically stable. Then, these conditions are generalised to the characterisation of all equilibrium points in an open region of the state space. Finally, an explicit lower bound on the exponential convergence rate, to an equilibrium, is derived.