Global exponential stability of impulsive discrete-time neural networks with time-varying delays

Abstract

This paper studies the problem of global exponential stability and exponential convergence rate for a class of impulsive discrete-time neural networks with time-varying delays. Firstly, by means of the Lyapunov stability theory, some inequality analysis techniques and a discrete-time Halanay-type inequality technique, sufficient conditions for ensuring global exponential stability of discrete-time neural networks are derived, and the estimated exponential convergence rate is provided as well. The obtained results are then applied to derive global exponential stability criteria and exponential convergence rate of impulsive discrete-time neural networks with time-varying delays. Finally, numerical examples are provided to illustrate the effectiveness and usefulness of the obtained criteria. Index TermsImpulsive discrete-time neural networks, global exponential stablity, exponential convergence rate, Halanay inequality.

Difference inequality for stability of impulsive difference equations with distributed delays

“…Recently, the asymptotic behaviors of impulsive difference equations have attracted considerable attention. Many interesting results on impulsive effect have been obtained [8][9][10][11].…”

A Halanay-type inequality approach to the stability analysis of discrete-time neural networks with delays

“…First, utilizing the Lyapunov stability theory we get a new discrete-time Halanay-type inequality, which considers more general difference inequality compared with that in [9,10,[34][35][36]. Based on the difference inequality obtained, we establish some new sufficient conditions for global exponential stability of discrete-time neural networks with time-varying delays, which generalizes the result considered in [9,28]. In addition, we apply the above results to discrete-time neural networks with impulsive perturbations and get sufficient conditions guaranteeing the globally exponential stability for such systems, which are less conservative to some extent compared with that in [30,34].…”

“…In [34], based on a new difference inequality, the exponential stability has been investigated for impulsive discrete-time stochastic bidirectional associative memory neural networks with time-varying delays. In [9], global exponential stability and exponential convergence rate has been studied for a class of impulsive discrete-time neural networks with time-varying delays. [30] has presented the global asymptotic and exponential stability of the equilibrium point of discrete-time delayed Hopfield neural networks with large impulse effects.…”

“…For example, in [9], the difference inequality is used for the stability analysis for discrete-time impulsive delay neural networks. But the difference inequality is under some restrictions on coefficients, which could be improved potentially.…”

“…In the past decades, neural networks and complex networks have been extensively studied and developed [1][2][3][4][5][6][7][8][9][10][11][12][13]. As artificial electronic systems, neural networks such as Hopfield neural networks, bidirectional neural networks and recurrent neural networks are frequently subject to impulsive perturbations and time delays which can affect dynamical behaviors of the systems.…”