Stability and synchronization analysis of neural networks via Halanay-type inequality

In this paper, not only some novel sufficient criteria for stability of discrete delay neural networks but also a new discriminant method for self synchronization of Hopfield neural networks are considered. Some novel stability criteria for discrete delay neural networks are obtained if the time average of the difference for two coefficients on some fixed lengths is lower bounded by some positive numbers. Moreover, a new discrete Halanay inequality is given, which extends the existing results. Based on the Halanay inequality, a novel sufficient criterion on self synchronization of Hopfield neural networks with time delay is obtained. Two numerical examples are given to demonstrate the effectiveness of proposed methods.