Conditions for global stability of some classes of nonsymmetric neural networks

In this paper we present new conditions ensuring global asymptotic stability (GAS) of the equilibrium point of neural networks. The results are valid both for symmetric and nonsymmetric interconnection matrices and allow for the consideration of all continuous nondecreasing neuron activation functions. Such functions may be unbounded (but not necessarily surjective), may have infinite intervals with zero slope as in a piece-wise-linear model, or both. The conditions for GAS are based on the concept of Lyapunov diagonally stable interconnection matrices and are proved via the Lyapunov direct method. In particular, a class of Lyapunov functions of the generalized Lur´e-Postnikov type is used instead of those currently employed in the literature. Several classes of interconnection matrices of applicative interest are shown to satisfy these conditions