Search

Abstract In this paper, based on the asymptotic expansion of Mittag-Leffler function and the fractional comparison principle, an improved fractional Halanay inequality with time-varying coefficients is proved by introducing parameters λ i and δ. The fractional autonomous Halanay inequality is generalized to the fractional non-autonomous case. Moreover, based on the improved fractional Halanay inequality and Lyapunov functional method, a novel sufficient condition on self synchronization of the fractional non-autonomous Hopfield neural networks with time delay is obtained. Finally, three numerical examples are given to demonstrate the effectiveness of proposed methods. [ABSTRACT FROM AUTHOR]

This paper focuses on the issue of robust stability analysis for recurrent neural networks (RNNs) with leakage delay. By constructing a novel Lyapunov-Krasovskii functional together with the reciprocally convex approach and the free-weighting matrix technique, some less conservative stability criteria in terms of linear matrix inequalities for RNNs are derived. The new contribution of this paper is that a novel delay-partitioning method is proposed, and some new zero equalities are introduced. Finally, several examples are given to demonstrate the effectiveness of the proposed methods. The simulated results reveal that the leakage delay has great influence on the dynamical systems, and it cannot be neglected. [ABSTRACT FROM AUTHOR]

This paper is concerned with the exponential stability of delayed neural networks. Combined the Legendre polynomials with free-weighting matrices technique, an improved free-matrix-based single integral inequality is given, which includes the general single integral inequality and the free-matrix-based single integral inequality as special cases. Furthermore, a free-matrix-based double integral inequality which improves the existing results is derived. As applications of these novel free-matrix-based integral inequalities, several exponential stability criteria with less conservatism for the delayed neural networks are obtained. The effectiveness of our main results is illustrated by three numerical examples from the literatures. [ABSTRACT FROM AUTHOR]

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]

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]