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Received Jan 31, 2013; Accepted Apr 7, 2013
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1. Introduction
In the past decades, neural networks (NNs) have attracted considerable attention due to their potential applications in associative memory, pattern recognition, optimization and signal processing, and so forth [1–3]. It is well known to us that stability is one of the preconditions in the design of neural networks. For example, if a neural network is employed to solve some optimization problems, it is highly desirable for the NNs to have a unique globally stable equilibrium. Therefore, stability analysis of NNs is a very important issue and has been studied extensively [4–11]. It is worth noting that most of the NNs have been analyzed by using a continuous-time model. However, when it comes to the implementation of continuous-time networks for the sake of computer-based simulation, experimentation or computation, it is necessary to discretize the continuous-time networks to formulate a discrete-time system. Under mild or no restriction on the discretization of step size, the dynamic characteristics of the continuous-time counterpart can be inherited by the discrete-time analogue to a certain extent, and the discrete-time model also remains similar to some other properties of the continuous-time system.
On the other hand, as a result of the finite switching speed of amplifiers and the inherent communication time of neurons, time delays are frequently encountered in neural networks in electronic implementations. Time delays can change the dynamic behaviors of neural networks evidently, which is very often the sources of instability, oscillation, and poor performance. Therefore, stability analysis of neural networks with time delays has been studied extensively during the past years; see [12–14] and the references therein. In practice, when modeling real neural systems, stochastic disturbances are probably part of the main sources leading to unwilling behaviors of neural networks. It has been proved that certain stochastic inputs could make the neural network unstable. Therefore, it is necessary to...