Uniform approximation of a class of impulsive delayed Hopfield neural networks on the half-line

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In this work, we investigate a uniform approximation of a nonautonomous delayed CNN-Hopfield-type impulsive system with an associated impulsive differential system where a partial discretization is introduced with the help of piecewise constant arguments. Sufficient conditions are formulated, which imply that the error estimate decays exponentially with time on the half-line [ 0 , ∞ ) . A critical step for the proof of this estimate is to show that, under the assumed conditions, the solutions of the Hopfield impulsive system are exponentially bounded and exponentially stable. A bounded coefficients case is also analyzed under simplified conditions. An example is presented and simulated in order to show the applicability of our conditions.