Discrete-time Cohen-Grossberg neural networks with transmission delays and impulses

Abstract

A discrete-time analogue is formulated for an impulsive Cohen-Grossberg neural network with
transmission delay in a manner in which the global exponential stability characterisitics of
a unique equilibrium point of the network are preserved. The formulation is based on
extending the existing semi-discretization method that has been implemented for computer
simulations of neural networks with linear stabilizing feedback terms. The exponential
convergence in the $p-$norm of the analogue towards the unique equilibrium point is
analysed by exploiting an appropriate Lyapunov sequence and properties of an $M-$matrix.
The main result yields a Lyapunov exponent that involves the magnitude and frequency of
the impulses. One can use the result for deriving the exponential stability of non-impulsive
discrete-time neural networks, and also for simulating the exponential stability of
impulsive and non-impulsive continuous-time networks.