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 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 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 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.     

Global robust exponential stability of delayed neural networks: An LMI approach

In this paper, the problems of determining the robust exponential stability and estimating the exponential convergence rate for neural networks with parametric uncertainties and time delay are studied. Based on Lyapunov–Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) technique, some delay-dependent criteria are derived to guarantee global robust exponential stability. The exponential convergence rate can be easily estimated via these criteria.     

On exponential stability analysis for neural networks with time-varying delays and general activation functions

This paper is concerned with the exponential stability analysis for a class of cellular neural networks with both interval time-varying delays and general activation functions. The boundedness assumption of the activation function is not required. The limitation on the derivative of time delay being less than one is relaxed and the lower bound of time-varying delay is not restricted to be zero. A new Lyapunov-Krasovskii functional involving more information on the state variables is established to derive a novel exponential stability criterion. The obtained condition shows potential advantages over the existing ones since no useful item is ignored throughout the estimate of upper bound of the derivative of Lyapunov functional. Finally, three numerical examples are included to illustrate the proposed design procedures and applications.     

Global exponential convergence for delayed cellular neural networks with a class of general activation functions

In this paper, we consider delayed cellular neural networks with a class of general activation functions. By using some mathematical analysis techniques, we establish new results to ensure that all solutions of the networks converge exponentially to zero point.     

变时滞Hopfield神经网络的周期解存在性及其全局指数稳定性

利用拓扑度理论中的连续性引理和推广Halanay不等式研究了变时滞的细胞神经网络的周期解的存在性及全局指数稳定性.给出了判别周期解及指数稳定性的代数判据,所得判据易于检验,具有广泛的实用性．同时,改进了已有文献的相关结论,最后通过数值例子说明结论的有效性．     

Global exponential stability for a class of neural networks

In this paper, the global exponential stability for a class of neural networks is investigated. A simple criterion ensuring global exponential stability is established, which is a less restrictive version of a recent criterion due to Park and Kwon. Some examples showing the effectiveness of the present criterion are given.     

Global exponential stability results for neutral-type impulsive neural networks

In this paper, by utilizing the Lyapunov–Krasovkii functional and combining with the linear matrix inequality (LMI) approach, we analyze the global exponential stability of neutral-type impulsive neural networks. In addition, an example is provided to illustrate the applicability of the result using LMI control toolbox in MATLAB.     

Novel robust stability criteria for uncertain stochastic Hopfield neural networks with time-varying delays

The problem of stochastic robust stability of a class of stochastic Hopfield neural networks with time-varying delays and parameter uncertainties is investigated in this paper. The parameter uncertainties are time-varying and norm-bounded. The time-delay factors are unknown and time-varying with known bounds. Based on Lyapunov–Krasovskii functional and stochastic analysis approaches, some new stability criteria are presented in terms of linear matrix inequalities (LMIs) to guarantee the delayed neural network to be robustly stochastically asymptotically stable in the mean square for all admissible uncertainties. Numerical examples are given to illustrate the effectiveness and less conservativeness of the developed techniques.     

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.     

Global exponential stability in Lagrange sense for recurrent neural networks with both time-varying delays and general activation functions via LMI approach

In this paper, we study the global exponential stability in a Lagrange sense for recurrent neural networks with both time-varying delays and general activation functions. Based on assuming that the activation functions are neither bounded nor monotonous or differentiable, several algebraic criterions in linear matrix inequality form for the global exponential stability in a Lagrange sense of the neural networks are obtained by virtue of Lyapunov functions and Halanay delay differential inequality. Meanwhile, the estimations of the globally exponentially attractive sets are given out. The results derived here are more general than that of the existing reference. Finally, two examples are given and analyzed to demonstrate our results.     

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 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 robust stability for delayed neural networks with polytopic type uncertainties

In this paper, global robust stability for delayed neural networks is studied. First the free-weighting matrices are employed to express the relationship between the terms in the system equation, and a stability condition for delayed neural networks is derived by using the S-procedure. Then this result is extended to establish a global robust stability criterion for delayed neural networks with polytopic type uncertainties. A numerical example given in [IEEE Trans Circuits Syst II 52 (2005) 33–36] for interval delayed neural networks is investigated. The effectiveness of the presented global robust stability criterion and its improvement over the existing results are demonstrated.     

Global robust stability for delayed neural networks with polytopic type uncertainties

In this paper, global robust stability for delayed neural networks is studied. First the free-weighting matrices are employed to express the relationship between the terms in the system equation, and a stability condition for delayed neural networks is derived by using the S-procedure. Then this result is extended to establish a global robust stability criterion for delayed neural networks with polytopic type uncertainties. A numerical example given in [IEEE Trans Circuits Syst II 52 (2005) 33–36] for interval delayed neural networks is investigated. The effectiveness of the presented global robust stability criterion and its improvement over the existing results are demonstrated.     

Existence and exponential stability of anti-periodic solutions of Hopfield neural networks with impulses

In this paper we investigate a class of Hopfield neural networks subject to periodic impulses. First we give sufficient conditions to ensure existence and exponential stability of the anti-periodic solutions, which are new and complementary to previously known results. Then we present an example to demonstrate our results.     

Robust exponential stability analysis of discrete-time switched Hopfield neural networks with time delay

The robust exponential stability problem in this paper for discrete-time switched Hopfield neural networks with time delay and uncertainty is considered. Firstly, the mathematical model of the system is established. Then by constructing a new Lyapunov–Krasovskii functional, some new delay-dependent criteria are developed, which guarantee the robust exponential stability of discrete-time switched Hopfield neural networks. A numerical example is provided to demonstrate the potential and effectiveness of the results obtained.