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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. [ABSTRACT FROM AUTHOR]

Auxiliary function-based summation inequalities are addressed in this technical note. By constructing appropriate auxiliary functions, several new summation inequalities are obtained. A novel sufficient criterion for asymptotic stability of discrete-time systems with time-varying delay is obtained in terms of linear matrix inequalities. The advantage of the proposed method is demonstrated by two classical examples from the literature. [ABSTRACT FROM AUTHOR]

In this paper, based on the discrete Wirtinger inequality, a novel summation inequality is established which extends the Jensen inequality. By the technique of the novel inequality, a sufficient criterion on asymptotic stability of discrete neural networks with time-varying delays is obtained. A numerical example is given to demonstrate the effectiveness of the inequality. [ABSTRACT FROM AUTHOR]