随机变时滞神经网络的全局渐近稳定性

研究了一类具有变时滞随机神经网络模型平衡点的全局渐近稳定性问题,通过构造李亚普诺夫函数并利用线性矩阵不等式理论,得出了随机变时滞神经网络的全局渐近稳定性的充分条件。     

具有时滞的细胞神经网络的稳定性

本文研究具有时滞的细胞神经网络的稳定性问题，利用构造李雅普诺夫泛函、常数变易法及不等式分析技巧，给出了时滞细胞神经网络全局渐近稳定性的充分条件。     

具有时滞的高阶Hopfield型神经网络的稳定性

通过Lyapunov泛函的方法，对具有时滞的高阶连续型Hopfield神经网络平衡点的稳定性进行分析，利用Razumikhin定理得到平衡点全局一致渐近稳定的时滞相关与时滞无关充分条件。     

具有时滞的细胞神经网络的稳定性

该文研究了具有时滞的细胞神经网络的稳定性问题,运用Lyapunov泛函法和Razumikhin法分别给出了时滞细胞神经网络全局渐近稳定的两个新的充分条件。其中,第一个条件与时延无关,而第二个条件与时延有关。获得的定理推广了已有文献中的结果,对于时滞细胞神经网络的硬件设计具有一定的指导意义。     

时滞细胞神经网络的稳定性研究

根据李雅普诺夫稳定性定理，利用不等式技巧，研究了具有时滞的细胞神经网络的稳定性，得到了与滞量无关的网络渐近稳定性的充分判据，该判据可用于时滞细胞神经网络的设计与检验，有重要的理论意义和应用价值。     

中立型BAM神经网络的鲁棒稳定性分析

本文主要研究不确定中立型BAM神经网络的鲁棒渐近稳定性问题, 不确定参数具有较范数有界更一般的线性分式形式, 考虑了中立时滞与状态时滞不相等的情况, 激励函数只要求满足有界和全局李普希兹条件,通过构造一个新的Lyapunov泛函, 利用Lyapunov-Krasovskii稳定性理论和一些不等式技术, 得到了具有较小约束的时滞中立型BAM神经网络的鲁棒渐近稳定性条件, 这个充分条件以线性矩阵不等式的形式给出, 容易验证.最后, 通过数值实例验证了所提算法的正确性和保守性.     

具反映扩散无穷连续分布时滞神经网络的全局渐近稳定性

利用同伦不变性原理、Dini导数、格林公式,研究了一类具反应扩散的无穷时滞神经网络系统的平衡点的存在唯一性和全局渐近稳定性.在去掉对神经元的激励函数有界性、可微性、去掉对平均时滞∫∞0sk(s)ds有界性的要求,仅要求激励函数满足Lipchitz条件等较宽松的条件下,获得了该类系统的全局渐近稳定性的充分条件.改进和推广了已有文献的最新结果.并用实例说明了这些获得的结果的有效性.     

基于LMI方法的时滞BAM神经网络的全局稳定性分析

对于时滞双向联想记忆(DBAM)神经网络的平衡点的稳定性问题,目前人们已经得到了很多富有意义的成果。该文提出一种新的神经网络模型标准神经网络模型(SNNM),通过状态的线性变换,将DBAM神经网络转化为时滞SNNM(DSNNM),并利用有关DSNNM的稳定性的一些结论,得到DBAM神经网络平衡点的全局渐近稳定性的充分条件。这些条件都以线性矩阵不等式(LMI)的形式给出,容易验证,保守性低。该方法扩展了以前的稳定性结果,同时也适用于其它类型的递归神经网络(时滞或非时滞)的稳定性分析。     

一类时变输入时滞不确定系统的鲁棒控制器设计

针对一类具有时变输入时滞的不确定系统,基于Lyapunov-Krasovskii方法,讨论了该类系统鲁棒控制器的设计问题.在不确定性满足范数有界条件下,给出了时滞相关的鲁棒可镇定充分条件及相应的鲁棒控制器设计方法,利用辅助变量和广义状态证明了闭环系统的渐近稳定性.最后,进行了数值仿真,结果证明了该方法的有效性和优越性.     

线性时滞系统的时滞相关稳定性

本文讨论了线性时滞系统x(t)=Ax( ) Bx(t-τ)渐近稳定的时滞界限，利用Lyapunov—Krasovskii泛函及H∞范数理论，获得了线性时滞系统时滞相关稳定的充分条件，同时得到了一个新的时滞界限的代数估计式。将本文结果应用于实际系统，计算简单，并且扩大了时滞的稳定区域，降低了对时滞的保守性。分析结果还表明，线性时滞系统的稳定性可以转化为一定常无时滞的线性系统的H∞控制问题。     

时延细胞神经网络的渐近稳定性条件

该文利用一个新的Liapunov函数,讨论了带时延细胞神经网络的全局渐近稳定性,得到了一些判定网络的全局渐近稳定新的充分条件,所得到的结果较之P.P.Civalleri等人的结果简单和实用且对于具体设计带时延细胞神经网络有重要的指导意义。     

Conditions of asymptotic stability for cellular neural networks with time delay

In this paper, global asymptotic stability for cellular neural networks with time delay is discussed using a novel Liapunov function. Some novel sufficient conditions for global asymptotic stability are obtained. Those results are simple and practical than those given by P. P. Civalleri, et al., and have a leading importance to design cellular neural networks with time delay.     

Stability of Hybrid Stochastic Retarded Systems

In the past few years, hybrid stochastic retarded systems (also known as stochastic retarded systems with Markovian switching), including hybrid stochastic delay systems, have been intensively studied. Among the key results, Mao proposed the Razumikhin-type theorem on exponential stability of stochastic functional differential equations with Markovian switching and its application to hybrid stochastic delay interval systems. However, the importance of general asymptotic stability has not been considered. This paper is to study Razumikhin-type theorems on general $p$-th moment asymptotic stability of hybrid stochastic retarded systems. The proposed theorems apply to complex systems including some cases when the existing results cannot be used.      

Parameter Conditions for Global Stability of FAST TCP

In this letter, we study the global asymptotic stability of FAST TCP in the presence of network feedback delays. Based on a continuous-time dynamic model of FAST TCP and a static approximation of queuing delay at the link, we derive stability conditions for FAST TCP. The derived conditions are explicitly appeared as tuning parameter conditions of FAST TCP, and hence can be satisfied in a distributed way. The simulation results illustrate the validity of the conditions for the global asymptotic stability.     

Global Uniform Asymptotic Stability of Competitive Neural Networks with Different-Time Scales and Delay

The global uniform asymptotic stability of competitive neural networks with different time scales and delay is investigated. By the method of variation of parameters and the method of inequality analysis, the condition for global uniformly asymptotically stable are given. A strict Lyapunov function for the flow of a competitive neural system with different time scales and delay is presented. Based on the function, the global uniform asymptotic stability of the equilibrium point can be proved.     

On Global Asymptotic Stability of Cohen–Grossberg Neural Networks With Variable Delays

This paper studies the problems of existence, uniqueness, global asymptotic stability and global exponential stability of the equilibrium of Cohen-Grossberg neural networks with variable delays. An estimation technique based on delay differential inequality with variable coefficients is developed to establish delay-independent/delay-dependent sufficient conditions for global asymptotic/exponential stability. The stability criteria obtained are based on the $M$-matrix theory. These criteria can be easily checked in practice and do not require that the delays be constant or differentiable. In particular, our delay-independent asymptotic/exponential stability criteria remove a restriction on the amplification functions imposed by the existing results. Furthermore, our delay-dependent exponential stability criteria give explicitly the allowable upper bound on the diagonal delays such that the global stability property of Cohen-Grossberg neural networks can be retained. Thus, our new results are of great importance in design and application of Cohen-Grossberg neural networks with variable delays. The effectiveness of the new results is further illustrated by two numerical examples in comparison with the existing results.      

一个带时延神经网络的分岔现象研究

本文借助中心流形定理详细讨论了一个带时延神经网络的Hopf分岔和周期解的渐近稳定性,给出了确定周期解的渐近稳定性、分岔方向,周期和解的渐近形式的一个算法,并进行了计算机仿真实验,仿真实验表明了所讨论的结果的有效性与正确性。     

Stability of differential multipass processes

Edwards' (1974) notion of stability along the pass for differential multipass processes is shown to be equivalent to what is known as pointwise asymptotic stability for delay differential systems     

Stability of cellular neural networks with delay

The problem of stability for cellular neural networks with delay (DCNNs) is studied. A new sufficient condition related to the global asymptotic stability for DCNNs is derived. This condition is less restrictive than that given in the literature