Exponential stability analysis for discrete-time impulsive delay neural networks with and without uncertainty

The purpose of this paper is to investigate the exponential stability for discrete-time impulsive delay neural networks and the robust exponential stability for discrete-time impulsive delay neural networks with uncertainty. By using Lyapunov functionals, first some new results on exponential stability for neural networks without uncertainty are presented, and then some results on robust exponential stability for neural networks with uncertainty are provided. Both the stability results that impulses act as perturbations and the stability results that impulses act as stabilizer are given. The obtained results have the virtue that they can deal with neural networks with any fixed time delay. Moreover, the impulsive interval is larger than 2 or the time delay is not needed in the main results. Some examples together with their simulations are also presented to show the effectiveness and the advantage of the obtained results.