Stabilizing Effects of Impulses in Discrete-Time Delayed Neural Networks

This brief studies the global exponential stability of the equilibrium point of discrete-time delayed Hopfield neural networks (DHNNs) with impulse effects by using difference inequalities. We shall consider the stabilizing effects of impulses when the corresponding impulse-free DHNN is even not asymptotically stable. The obtained results characterize the aggregated effects of impulses and deviation of the impulse-free DHNN from its equilibrium point on the exponential stability of the whole system. It is shown that, because of effects of impulses, the impulsive discrete-time DHNN may be exponentially stable even if the evolution of impulse-free component deviates from its equilibrium point exponentially.