New stability conditions for neural networks with constant and variable delays

In this paper, by utilizing Lyapunov functional method, we analyze global asymptotic stability of neural networks with constant delays. A new sufficient condition ensuring global asymptotic stability of the unique equilibrium point of delayed neural networks is obtained. Furthermore, based on the method of delay differential inequality, the conditions checking global exponential stability of the equilibrium point of neural networks with variable delays are given. The results extend and improve the earlier publications.     

Exponential stability for nonautonomous neural networks with variable delays

In this paper, by utilizing a delay differential inequality and combining with inequality analysis technique, we investigate global exponential stability for nonautonomous neural networks with variable delays. Some new sufficient conditions ensuring global exponential stability are obtained. An example is also given to demonstrate the effectiveness of the obtained results.     

New delay-dependent global robust stability conditions for interval neural networks with time-varying delays

This paper deals with the problem of delay-dependent global robust stability analysis for interval neural networks with time-varying delays. By introducing an equivalent transformation of interval systems and the free-weighting matrix technique, a new delay-dependent condition on global robust stability is established. This condition is presented in terms of a linear matrix inequality (LMI), which can be easily checked by using recently developed algorithms in solving LMIs. A numerical example is provided to demonstrate the effectiveness of the proposed method.     

New LMI conditions for global exponential stability of cellular neural networks with delays

In this paper, we investigate further cellular neural networks model with delays. We allow the model to have nondifferentiable and unbounded signal function, and use linear matrix inequality (LMI) framework and Homeomorphism theorem to prove the existence and uniqueness of the equilibrium, and derive some new sufficient condition ensuring global exponential stability of the networks. Two examples with their numerical simulations are provided to show the correctness of our analysis. It is believed that these results are significant and useful for the design and applications of cellular neural networks.     

New stability criteria for neural networks with time-varying delays

This paper is concerned with the stability analysis problem of neural networks with time delays. The delay intervals [−d(t), 0] and [−h, 0] are divided into m subintervals with equal length. Some free matrices are introduced to build the relationship among the elements of the resultant matrix inequalities. With the above operations, the new stability criteria are built for the general class of neural networks. The conditions are presented in the form of linear matrix inequalities (LMIs), which can be solved by the numerically efficient Matlab LMI toolbox. Several examples are provided to show that our methods are much less conservative than recently reported ones.     

Global exponential stability of interval neural networks with variable delays

In this work, the conditions ensuring existence, uniqueness, and global exponential stability of the equilibrium point of interval neural networks with variable delays are studied. Applying the idea of the vector Lyapunov function, and M-matrix theory, the sufficient conditions for global exponential stability of interval neural networks are obtained.     

Global exponential stability of Cohen-Grossberg neural networks with variable delays

A class of generalized Cohen-Grossberg neural networks（CGNNs） with variable de- lays are investigated. By introducing a new type of Lyapunov functional and applying the homeomorphism theory and inequality technique, some new conditions axe derived ensuring the existence and uniqueness of the equilibrium point and its global exponential stability for CGNNs. These results obtained are independent of delays, develop the existent outcome in the earlier literature and are very easily checked in practice.     

New robust stability criteria for uncertain neural networks with interval time-varying delays

In this paper, problem of robust stability of uncertain neural networks with interval time-varying delays has been investigated. The delay factor is assumed to be time-varying and belongs to a given interval, which means that the lower and upper bounds of the interval time-varying delays are available. Based on the Lyapunov–Krasovskii functional approach, a new delay-dependent stability criteria is presented in terms of linear matrix inequalities (LMIs). Two numerical examples are given to illustrate the effectiveness of the proposed method.     

Delay-dependent asymptotic stability for neural networks with distributed delays

In this paper, dynamical behavior of a class of neural networks with distributed delays is studied by employing suitable Lyapunov functionals, delay-dependent criteria to ensure local and global asymptotic stability of the equilibrium of the neural networks. Our results are applied to classical Hopfield neural networks with distributed delays and some novel asymptotic stability criteria are also derived. The obtained conditions are shown to be less conservative and restrictive than those reported in the known literature.     

New results on global asymptotic stability analysis for neural networks with time-varying delays

This note provides new results on global asymptotic stability for neural networks with time-varying delay. Two types of time-varying delay are considered: one is differentiable and has bounded derivative; the other one is continuous and may vary very fast. By introducing an augmented Lyapunov–Krasovskii functional, new delay-dependent stability criteria for delayed neural networks are derived in terms of linear matrix inequalities (LMIs). It is shown that the obtained criteria can provide less conservative results than some existing ones. Numerical examples are given to demonstrate the applicability of the proposed approach.     

New results of global robust exponential stability of neural networks with delays

In this paper, the global robust exponential stability of interval neural networks with delays is investigated. Employing homeomorphism techniques and Lyapunov functions, we establish some sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point for delayed neural networks. It is shown that the obtained results improve and generalize the previously published results.     

Robust stability for stochastic Hopfield neural networks with time delays

In this paper, the asymptotic stability analysis problem is considered for a class of uncertain stochastic neural networks with time delays and parameter uncertainties. The delays are time-invariant, and the uncertainties are norm-bounded that enter into all the network parameters. The aim of this paper is to establish easily verifiable conditions under which the delayed neural network is robustly asymptotically stable in the mean square for all admissible parameter uncertainties. By employing a Lyapunov–Krasovskii functional and conducting the stochastic analysis, a linear matrix inequality (LMI) approach is developed to derive the stability criteria. The proposed criteria can be checked readily by using some standard numerical packages, and no tuning of parameters is required. Examples are provided to demonstrate the effectiveness and applicability of the proposed criteria.     

Dynamical analysis of fuzzy BAM neural networks with variable delays

In this work, employing Lyapunov functional and elemental inequality ($2ab leqslant ra^2 + tfrac{1} {r}b^2$2ab leqslant ra^2 + tfrac{1} {r}b^2, r > 0), some sufficient conditions are derived for the existence and uniqueness of periodic solution of fuzzy bidirectional associated memory (BAM) neural networks with variable delays. Some new and simple criteria are obtained to ensure global exponential stability of periodic solution, which are important in design and applications of fuzzy BAM neural networks.     

时滞Hopfield神经网络的全局指数稳定性

讨论带有可变时滞的Hopfield神经网络的全局指数稳定性.在非线性激励函数满足Lipschitz条件的假设下,利用推广的Halanay不等式,Dini导数和分析技巧,建立了这类神经网络系统全局指数稳定的几个判别准则.这些判别准则仅仅依赖于系统的参数.     

具有时滞的一般型脉冲神经网络的指数稳定性

讨论具有时滞的一般性脉冲神经网络的稳定性.在不假定激励函数有界或可导的前提下,利用非光滑分析和Lyapunov泛函,得到了这类神经网络系统平衡点的存在唯一性和全局指数稳定性判别准则.作为特例,得到了Hopfield神经网络,时滞细胞神经网络,双向联想记忆神经网络的平衡点的存在唯一性和全局指数稳定性判定定理.     

Global exponential stability for nonautonomous cellular neural networks with unbounded delays

Global exponential stability of nonautonomous cellular neural networks with unbounded delays is considered in this paper. By applying Lyapunov functional method, some new sufficient conditions are given for global exponential stability of solutions of the networks. The stability conditions obtained here improve and extend some of the previous conditions. An example is presented to illustrate the applicability of these conditions.     

Novel delay-dependent asymptotic stability criteria for neural networks with time-varying delays

The problem of delay-dependent asymptotic stability criteria for neural networks (NNs) with time-varying delays is investigated. An improved linear matrix inequality based on delay-dependent stability test is introduced to ensure a large upper bound for time-delay. A new class of Lyapunov function is constructed to derive a novel delay-dependent stability criteria. Finally, numerical examples are given to indicate significant improvement over some existing results.     

Exponential stability analysis for uncertain neural networks with interval time-varying delays

In this paper, the problem of exponential stability analysis for neural networks is investigated. It is assumed that the considered neural networks have norm-bounded parametric uncertainties and interval time-varying delays. By constructing a new Lyapunov functional, new delay-dependent exponential stability criteria with an exponential convergence rate are established in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Two numerical examples are included to show the effectiveness of proposed criteria.     

Invariant and attracting set of fuzzy cellular neural networks with variable delays

The aim of this paper is to study the invariant and attracting set of fuzzy cellular neural networks with variable delays. Based on a delayed differential inequality and the properties fuzzy logic operation and M-matrix, the invariant and attracting set is obtained. Moreover, two examples are given to illustrate the effectiveness of our theoretical result.