Improved stability criteria for a class of neural networks with variable delays and impulsive perturbations

Keywords: Neural networks Exponential stability M-matrix Variable delays Impulses a b s t r a c t This paper further investigates the problem of stability analysis for a kind of neural networks with variable delays and nonlinear impulses. With the help of M-matrix, the homeo-morphism theory, some effective inequalities and analysis techniques, certain novel criteria on the existence, uniqueness and exponential stability of the equilibrium point have been established. Moreover, these criteria possess adjustable real parameters, which extend and improve many existing results in the literature. In the end, two numerical examples are provided to illustrate the validation of the theoretical results. Over the past few decades, several kinds of neural networks [1–3] such as Hopfield neural networks, cellular neural networks , bidirectional associative memory neural networks (for short by HNNs, CNNs, BAMNNs, respectively) have received considerable attentions because of their great potential applications in areas of signal processing, pattern recognition, asso-ciative memory and optimization [4,5]. As we know, during the hardware implementation of neural networks, time delays are inevitable due to finite switching speeds of the amplifiers and communication time, which may bring about complex influence on the system such as oscillation and instability [6]. On the other hand, impulsive effects widely exist in many realistic networks [7,8], which may be caused by witching phenomenon, sudden changes, or other unexpected noise. Therefore, it is more appropriate to take both delays and impulsive effects into account when modeling neural networks, and lots of important stability results have been reported on HNNs, CNNs, BAMNNs with delays and impulses. One can refer to [9– 21] and references therein. Recently, authors in [22] introduced a neural network of general type, which incorporated impulsive delayed HNNs, CNNs, BAMNNs as its special cases by choosing suitable nonlinear terms f i ð; Þ and was formulated by the following form: