Global stability of a class of discrete-time recurrent neural networks

This paper presents several analytical results on global asymptotic stability (GAS) and global exponential stability (GES) for the equilibrium states of a general class of discrete-time recurrent neural networks (DTRNNS) with asymmetric connection weight matrices and globally Lipschitz continuous and monotone nondecreasing activation functions. A necessary and sufficient condition is formulated to guarantee the existence and uniqueness of equilibria of such DTRNNS. The obtained results are less restrictive, different from, and improve upon the existing ones on GAS and GES of neural networks with special classes of activation functions.