Asymptotical stability in discrete-time neural networks

In this work, we present a proof of the existence of a fixed point and a generalized sufficient condition that guarantees the stability of it in discrete-time neural networks by using the Lyapunov function method. We also show that for both symmetric and asymmetric connections, the unique attractor is a fixed point when several conditions are satisfied. This is an extended result of Chen and Aihara (see Physica D, vol. 104, no. 3/4, p. 286-325, 1997). In particular, we further study the stability of equilibrium in discrete-time neural networks with the connection weight matrix in form of an interval matrix. Finally, several examples are shown to illustrate and reinforce our theory.