A new criterion for global robust stability of interval neural networks with discrete time delays

This paper further studies global robust stability of a class of interval neural networks with discrete time delays. By introducing an equivalent transformation of interval matrices, a new criterion on global robust stability is established. In comparison with the results reported in the literature, the proposed approach leads to results with less restrictive conditions. Numerical examples are also worked through to illustrate our results.     

Global robust exponential stability analysis for stochastic interval neural networks with time-varying delays

In this paper, the global exponential stability is investigated for a class of stochastic interval neural networks with time-varying delays. The parameter uncertainties are assumed to be bounded in given compact sets. Based on Lyapunov stable theory and stochastic analysis approaches, the delay-dependent criteria are derived to ensure the global, robust, exponential stability of the addressed system in the mean square. The criteria can be checked easily by the LMI control toolbox in Matlab. A numerical example is given to illustrate the effectiveness and improvement over some existing results.     

Global robust stability of interval cellular neural networks with time-varying delays

This paper studies the global robust asymptotic stability (GRAS) and global robust exponential stability (GRES) of delayed cellular neural networks with time-varying delays. A series of new criteria concerning GRAS and GRES are obtained by employing the Young's inequality, Halanay's inequality and Lyapunov functional and combine with some analysis techniques. Several previous results are improved and generalized. Some examples and remarks are also given to illustrate the effectiveness of the results. In addition, these criteria possess important leading significance in design and applications of global stable DCNNs, and are of great interest in many applications.     

Global exponential stability of neutral-type impulsive neural networks with discrete and distributed delays

In this paper, the global exponential stability for neutral-type impulsive neural networks with discrete and distributed delays is established by utilizing the Lyapunov–Krasovskii functional combining with the linear matrix inequality(LMI) approach.     

Global exponential stability of reaction-diffusion cellular neural networks with S-type distributed time delays

The authors discuss the existence of the equilibrium point and its global exponential stability of reaction-diffusion cellular neural networks (RDCNNs) with S-type distributed signal transmission delays along the axon of a neuron by means of the topological degree theory and differential inequality technique. A theorem and two corollaries were obtained in which the boundedness, monotonicity and differentiability conditions on the activation functions are not required. The sufficient conditions on global exponential stability established in this paper, which are easily verifiable, have a wider adaptive range.     

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.     

Global exponential stability in Lagrange sense for recurrent neural networks with time delays

In this paper, we study the global exponential stability in Lagrange sense for continuous recurrent neural networks (RNNs) with multiple time delays. Three different types of activation functions are considered, which include both bounded and unbounded activation functions. By constructing appropriate Lyapunov-like functions, we provide easily verifiable criteria for the boundedness and global exponential attractivity of RNNs. These results can be applied to analyze monostable as well as multistable neural networks.     

Further analysis on global robust exponential stability of neural networks with time-varying delays

In this paper, an approach based on H-matrix theory and Halanay inequality is developed to present a sufficient condition for global robust exponential stability of interval neural networks with time-varying delays. Theoretic analysis shows that our result includes a previous result derived in the literature. Finally, some numerical examples are given to show the effectiveness of the obtained results.     

Global robust stability for stochastic interval neural networks with continuously distributed delays of neutral type

In this paper, by using the Lyapunov-Krasovskii functional method, we investigate the global robust stability for stochastic interval neural networks with continuously distributed delays of neutral type. Some new stability criteria are presented in terms of linear matrix inequality (LMI). Two numerical examples are also given to show the effectiveness of the obtained results using LMI control toolbox in MATLAB.     

Global exponential stability analysis on impulsive BAM neural networks with distributed delays

Using M-matrix and topological degree tool, sufficient conditions are obtained for the existence, uniqueness and global exponential stability of the equilibrium point of bidirectional associative memory (BAM) neural networks with distributed delays and subjected to impulsive state displacements at fixed instants of time by constructing a suitable Lyapunov functional. The results remove the usual assumptions that the boundedness, monotonicity, and differentiability of the activation functions. It is shown that in some cases, the stability criteria can be easily checked. Finally, an illustrative example is given to show the effectiveness of the presented criteria.     

Global asymptotic stability analysis for neutral stochastic neural networks with time-varying delays

In this paper, the global asymptotic stability is investigated for a class of neutral stochastic neural networks with time-varying delays and norm-bounded uncertainties. Based on Lyapunov stability theory and stochastic analysis approaches, delay-dependent criteria are derived to ensure the global, robust, asymptotic stability of the addressed system in the mean square for all admissible parameter uncertainties. The criteria can be checked easily by the LMI Control Toolbox in Matlab. A numerical example is given to illustrate the feasibility and effectiveness of the results.     

Global asymptotic stability analysis for integro-differential systems modeling neural networks with delays

In this paper, the global asymptotic stability of the equilibrium point of integro-differential systems modeling neural networks with time-varying delays are studied. Proper Lyapunov functionals and some analytic techniques are employed to derive the sufficient conditions under which the networks proposed are the global asymptotic stability. The results have shown to improve the previous global asymptotic stability results derived in the literature. Some examples are given to illustrate the correctness of our results.     

Global exponential stability and global attractivity of impulsive Hopfield neural networks with time delays

In this paper, by means of constructing the extended impulsive delayed Halanay inequality and by Lyapunov functional methods, we analyze the global exponential stability and global attractivity of impulsive Hopfield neural networks with time delays. Some new sufficient conditions ensuring exponential stability of the unique equilibrium point of impulsive Hopfield neural networks with time delays are obtained. Those conditions are more feasible than that given in the earlier references to some extent. Some numerical examples are also discussed in this work to illustrate the advantage of the results we obtained.     

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 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.     

Global exponential stability of Hopfield neural networks with distributed delays

In this paper, dynamical behaviors of Hopfield neural networks system with distributed delays were studied. By using contraction mapping principle and differential inequality technique, a sufficient condition was obtained to ensure the existence uniqueness and global exponential stability of the equilibrium point for the model. Here we point out that our methods, which are different from previous known results, base on the contraction mapping principle and inequality technique. Two remarks were also worked out to demonstrate the advantage of our results.     

Global exponential stability analysis of bidirectional associative memory neural networks with time-varying delays

In this paper, global exponential stability is studied for a class of high-order bidirectional associative memory (BAM) neural networks with time-varying delays. An approach combining the Lyapunov functional with the Linear Matrix Inequality (LMI) is taken to study the problems. Several sufficient conditions are presented for ensuring the system to be globally exponentially stable. Three typical examples are presented to show the application of the criteria obtained in this paper.     

Global asymptotic stability of stochastic fuzzy cellular neural networks with multiple discrete and distributed time-varying delays

In this paper, the Takagi–Sugeno (T–S) fuzzy model representation is extended to the stability analysis for stochastic cellular neural networks with multiple discrete and distributed time varying delays. A novel linear matrix inequality (LMI) based stability criterion is derived to guarantee the asymptotic stability of stochastic cellular neural networks with multiple discrete and distributed time varying delays which are represented by T–S fuzzy models. The derived delay-dependent stability conditions are based on free-weighting matrices method, Lyapunov stability theory and LMI technique. In fact, these techniques lead to generalized and less conservative stability condition that guarantee the wide stability region. The delay-dependent stability condition is formulated, in which the restriction of the derivative of the time-varying delay is removed. Our results can be specialized to several cases including those studied extensively in the literature. Finally, numerical examples are given to demonstrate the effectiveness and conservativeness of our results.