New delay-dependent global asymptotic stability criteria of delayed Hopfield neural networks

In this paper, the global asymptotic stability of Hopfield neural networks (HNNs) with delays is investigated by utilizing Lyapunov functional method and the linear matrix inequality (LMI) technique. Distinct difference from other analytical approaches lies in “linearization” of the neural network model, by which the considered neural network model is transformed into a linear time-variant system. Then, a process, which is called parameterized first-order model transformation, is used to transform the linear system. Novel criteria for global asymptotic stability of the unique equilibrium point of delayed HNNs are obtained. The results are related to the size of delays. The obtained results are less conservative and restrictive than those established in the earlier references. Two numerical examples are given to show the effectiveness of our proposed method.