含离散和分布时变时延神经网络系统的指数稳定性

针对一类含有离散和分布时延神经网络,在神经激活函数较弱的约束条件下,通过定义一个更具一般性的Lyapunov泛函,使用凸组合技术,得到了新的基于线性矩阵不等式表示的指数稳定性判据.与现有结果相比,这些判据具有较小的保守性.仿真算例表明,得到的结果是有效的且保守性小.     

Global Exponential Stability Analysis of Discrete‐Time Genetic Regulatory Networks with Time Delays

This paper focuses on the study of global robust exponential stability of discrete‐time genetic regulatory networks (GRNs) with time‐invariant/time‐varying delays and parameter uncertainties. Many existing results on this problem are based on the linear matrix inequality (LMI) approach, which needs to verify whether there exists a feasible solution of a set of LMIs. Along with the increase in the number of genes, dimensions of LMIs will increase accordingly, which will lead to a large amount of calculation. Based on M‐matrix theory, sufficient conditions ensuring the global robust exponential stability of a class of discrete‐time GRNs with time‐invariant/time‐varying delays and parameter uncertainties are presented. These given conditions are to check whether a constructed constant matrix is a nonsingular M‐matrix. Simulation results of several examples are given to demonstrate the validity of the proposed method.     

Decentralized Event-triggered Stability Analysis of Neutral-type BAM Neural Networks with Markovian Jump Parameters and Mixed Time Varying Delays

This paper investigates decentralized event-triggered stability analysis of neutral-type BAM neural networks with Markovian jump parameters and mixed time varying delays. We apply the decentralized event triggered approach to the bidirectional associative memory (BAM) neural networks to reduce the network traffic and the resource of computation. A bidirectional associative memory neural networks is constructed with the mixed time varying delays and Markov process parameters. The criteria for the asymptotically stability are proposed by using with the Lyapunov-Krasovskii functional method, reciprocal convex property and Jensen’s inequality. Stability condition of neutral-type BAM neural networks with Markovian jump parameters and mixed delays is established in terms of linear matrix inequalities. Finally three numerical examples are given to demonstrate the effectiveness of the proposed results     

On p-th Moment Exponential Stability for Stochastic Cellular Neural Networks with Distributed Delays

International Journal of Control, Automation and Systems - In this paper, a class of stochastic cellular neural networks with distributed delays are investigated. With the help of the method of...     

一类时滞神经网络的全局指数稳定性

利用M-矩阵和拓扑学等有关知识,通过构建向量李雅普诺夫函数,研究了一类包含分布时滞和可变时滞的神经网络的平衡点的存在性、唯一性及其全局指数稳定性。在没有假定激励函数有界、可微的情况下,得到了该类神经网络平衡点的存在性、唯一性及其在平衡点全局指数稳定的充分判据。该判据计算简便,且与时间滞后量无关,便于在实践中应用。文中给出了一个算例。     

Global Exponential Stability for Impulsive BAM Neural Networks with Distributed Delays on Time Scales

In this paper, by utilizing the time scale calculus theory, topological degree theory and Hölder’s inequality on time scales, we analyze a class of impulsive BAM neural networks with distributed delays on time scales. Some sufficient conditions are obtained to ensure the existence, uniqueness and the global exponential stability of the equilibrium point. Finally, an example is provided to demonstrate the effectiveness of the results.     

Mean-Square Exponential Input-to-State Stability of Stochastic Gene Regulatory Networks with Multiple Time Delays

Neural Processing Letters - This paper is concerned with the input-to-state stability of stochastic gene regulatory networks with multiple time delays. It is well acknowledged that stochastic...     

Exponential Stability on Stochastic Neural Networks With Discrete Interval and Distributed Delays

This brief addresses the stability analysis problem for stochastic neural networks (SNNs) with discrete interval and distributed time-varying delays. The interval time-varying delay is assumed to satisfy $0≪d_{1}leq d(t) leq d_{2}$ and is described as $d(t)= d_{1}+h(t)$ with $0leq h(t) leq d_{2}-d_{1}$. Based on the idea of partitioning the lower bound $d_{1}$, new delay-dependent stability criteria are presented by constructing a novel Lyapunov–Krasovskii functional, which can guarantee the new stability conditions to be less conservative than those in the literature. The obtained results are formulated in the form of linear matrix inequalities (LMIs). Numerical examples are provided to illustrate the effectiveness and less conservatism of the developed results.      

Global Robust Exponential Stability of Uncertain Neutral High-Order Stochastic Hopfield Neural Networks with Time-Varying Delays

In this paper, a class of uncertain neutral high-order stochastic Hopfield neural networks with time-varying delays is investigated. By using Lyapunov-Krasovskii functional and stochastic analysis approaches, new and less conservative delay-dependent stability criteria is presented in terms of linear matrix inequalities to guarantee the neural networks to be globally robustly exponentially stable in the mean square for all admissible parameter uncertainties and stochastic perturbations. Numerical simulations are carried out to illustrate the main results.     

New Results on Robust Exponential Stability of Uncertain Stochastic Neural Networks with Mixed Time-Varying Delays

This letter considers the robust exponential stability of uncertain stochastic neural networks with mixed time-varying delays. By using Lyapunov–Krasovskii functional and Itô’s differential formula, several new sufficient conditions guaranteeing the global robust exponential stability are derived in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness and less conservativeness of our results.     

Further Improvement on Delay-Dependent Global Robust Exponential Stability for Delayed Cellular Neural Networks with Time-Varying Delays

Neural Processing Letters - This paper is concerned with global robust exponential stability for a class of delayed cellular neural networks with time-varying delays. Some new sufficient conditions...     

一类具有变时滞的Hopfield型神经网络的全局指数稳定性

通过构造适当的Lyapunov函数,利用Halanay不等式和Young不等式,讨论一类具有变时滞的Hopfield型神经网络的全局指数稳定性.在对网络施加两个不同的神经元激励函数的条件下,导出网络全局指数稳定的一个充分条件,得到的充分条件在实际应用中易于验证,且有较小的保守性,因而对网络的应用和设计具有重要意义.最后,一个数值实例进一步验证结果的正确性.     

变时滞神经网络的全局指数稳定性

利用M矩阵理论,同构理论以及不等式技巧,研究了一类变时滞神经网络平衡点的存在性和惟一性问题。同时利用M矩阵理论,反证法以及不等式技巧,得到了变时滞神经网络系统惟一的平衡点的全局指数稳定性的充分条件。通过判断由神经网络的权系数、自反馈函数以及激励函数构造的矩阵是否为M矩阵,即可以检验该变时滞神经网络系统的全局指数稳定性。该判据易于用Matlab进行检验,最后给出一个仿真示例进一步证明了判据的有效性。     

Robust Stability for Uncertain Delayed Fuzzy Hopfield Neural Networks With Markovian Jumping Parameters

This paper is concerned with the problem of the robust stability of nonlinear delayed Hopfield neural networks (HNNs) with Markovian jumping parameters by Takagi-Sugeno (T-S) fuzzy model. The nonlinear delayed HNNs are first established as a modified T-S fuzzy model in which the consequent parts are composed of a set of Markovian jumping HNNs with interval delays. Time delays here are assumed to be time-varying and belong to the given intervals. Based on Lyapunov-Krasovskii stability theory and linear matrix inequality approach, stability conditions are proposed in terms of the upper and lower bounds of the delays. Finally, numerical examples are used to illustrate the effectiveness of the proposed method.     

时滞脉冲型Hopfield神经网络的全局指数稳定性*

基于众多领域及生物神经网络本身所存在的脉冲瞬动现象，本文首次提出并研究了带时滞的脉冲型Ｈｏｐｆｉｅｌｄ神经网络的全局指定稳定性问题，并讨论了其平衡态的存在唯一性。     

Global Robust Exponential Stability of Interval Neural Networks with Delays

In this Letter, based on globally Lipschitz continous activation functions, new conditions ensuring existence, uniqueness and global robust exponential stability of the equilibrium point of interval neural networks with delays are obtained. The delayed Hopfield network, Bidirectional associative memory network and Cellular neural network are special cases of the network model considered in this Letter. This revised version was published online in June 2006 with corrections to the Cover Date.     

Exponential Stability of Positive Recurrent Neural Networks with Multi-proportional Delays

Neural Processing Letters - This paper presents some new results on the existence, uniqueness and generalized exponential stability of a positive equilibrium for positive recurrent neural networks...     

Delay-Dependent Exponential Stability of Cellular Neural Networks with Multi-Proportional Delays

Global exponential stability of a class of cellular neural networks with multi-proportional delays is investigated. New delay-dependent sufficient conditions ensuring global exponential stability for the system presented here are related to the size of the proportional delay factor, by employing matrix theory and Lyapunov functional, and without assuming the differentiability, boundedness and monotonicity of the activation functions. Two examples and their simulation results are given to illustrate the effectiveness of the obtained results.     

Design of Stochastic Passivity and Passification for Delayed BAM Neural Networks with Markov Jump Parameters via Non-uniform Sampled-Data Control

Neural Processing Letters - This paper investigates the issue of passivity and passification for delayed Markov jump bidirectional associate memory (BAM)-Type neural networks via non-uniform...     

脉冲时滞Hopfield神经网络的全局指数稳定性

研究一类具有脉冲控制的时滞Hopfideld神经网络的全局指数稳定性,通过Lyapunov-Krasovskii稳定性理论和Halanay不等式等方法,构造合适的Lyapunov泛函,利用不等式技巧得到了确保时滞神经网络在脉冲控制下全局指数稳定的一个充分条件,保证了Hofidd神经网络在脉冲控制下的全局指数稳定,并估计了系统的指数收敛率.为了便于计算和验证结论的有效性,给出一个简化的充分条件.最后通过数值实例的实验仿真证实了结论的有效性、可行性.