具有反馈时延的TCP Vega s 拥塞控制算法的稳定性分析

将Internet拥塞控制算法看作一个复杂的动态非线性反馈系统，借助多变量频率域控制系统的广义Nyquist判据和时延微分方程的Pontryagin判据，研究了各通信回路时延相同和时延不同条件下Internet网络拥塞控制算法，得到了具有反馈时延的TCP Vegas拥塞控制算法在平衡点渐近稳定的多个判据。仿真结果说明了稳定性判据的有效性和实用性。     

离散Hopfield联想记忆神经网络的渐近行为

该文对一类离散Hopfield联想记忆神经网络的渐近行为进行了讨论，首先提出这类I／O函数取为Sigmoid型函数的离散Hopfield联想记忆神经网络的数学模型，讨论并给出了这种模型的一系列性质，例如运动轨迹的有界性，平衡点的唯一性以及渐近稳定性等，得到了平衡点渐近稳定的充分条件，检验这种神经网络模型的渐近稳定性，只需要测试一个特定矩阵的定性性质或特定不等式即可，这些结果可用于离散Hopfield联想记忆神经网络的综合过程。     

离散Hopfield双向联想记忆神经网络的稳定性分析

首先将离散Hopfield双向联想记忆神经网络转化成一个特殊的离散Hopfield网络模型.在此基础上,对离散Hopfield双向联想记忆神经网络的全局渐近稳定性和全局指数稳定性进行了新的分析.证明了神经网络连接权矩阵在给定的约束条件下有唯一的而且是渐近稳定的平衡点.利用Lyapunov方程正对角解的存在性得到了几个判定平衡点为全局渐近稳定和全局指数稳定的充分条件.这些条件可以用于设计全局渐近稳定和全局指数稳定的神经网络.所做的分析扩展了以前的稳定性结果.     

具有有界输入的网络控制系统时延独立稳定性

基于有界时延、无数据包丢失、传感器时钟驱动、执行器事件驱动,文章提出了用一个特定的实值函数来调节动态输出反馈控制器的输出以确保控制对象输入有界的方法,建立了具有分布时延、有界输入、动态输出反馈网络控制系统的非线性数学模型.用李雅普诺夫第二方法和线性矩阵不等式描述分析了系统的渐近稳定性,并推导出与时延无关的系统渐近稳定的充分条件.最后MATLAB仿真算例说明：稳定判据是可行的,有界输入的控制方法是有效的.     

几类动态反馈神经网络的稳定性分析

稳定性分析是动态反馈神经网络的重要研究内容 ,对于网络的设计和应用具有指导作用。本文针对几类典型的动态反馈神经网络模型 ,包括离散网络、非对称网络和时延网络 ,利用 L yapunov方法得到了网络的稳定条件     

时延细胞神经网络的全局渐近稳定性

通过构造新的Lyapunov泛函,在Lyapunov泛函中巧妙引入可调的实参数,并结合不等式运用的一些技巧,讨论了时延细胞神经网络的全局渐近稳定性问题,得到了该模型的平衡点全局渐近稳定的一些新的充分条件。所得的结果改进推广了已有文献中相应的一些结论,并且可应用于以前所不能处理的若干情形。理论分析和数学推导表明,全局渐近稳定性的一个简单充分判据与时延是有关的。所得结果突出了时延对于细胞神经网络的全局渐近稳定性的影响,这对于设计带时延的细胞神经网络有着重要的参考价值。此外,通过实例说明了相应结果的应用,这在理论上和应用中都有着重要的意义。     

动态神经网络的输入2状态稳定性分析

针对非自治的动态神经网络系统，建立了动态神经网络的数学模型．并将其等效成一个非线性仿射控制系统．深入分析了该系统平衡点的存在性、唯一性和全局渐近稳定性，给出了系统输入-状态稳定的充分条件，构建了ISS-Lyapunov函数，并应用该函数确保了系统的全局渐近稳定性．     

具有随机时延和丢包补偿的NCS的H∞控制

给出一个存在随机时延和数据包丢失的网络控制系统（Networked Control System, NCS）模型，并分析了其渐近稳定的LMI条件．为了降低数据包丢失对系统稳定性的影响，在系统中增加了补偿器，并建立了具有丢包补偿器和随机网络诱导时延的NCS模型．在此模型的基础上，给出了系统渐近稳定和γ次优、最优的充分条件，并且获得了系统最优H∞控制的输出反馈控制律．对同一算例进行Matlab仿真，结果表明具有丢包补偿器的NCS趋于稳定的速度更快．     

二阶神经网络的全局指数稳定性分析

当神经网络应用于最优化计算时,理想的情形是只有一个全局渐近稳定的平衡点,并且以指数速度趋近于平衡点,从而减少神经网络所需计算时间,二阶神经网络较一般神经网络具有更快的收敛速度,对于二阶连续型Hopfield神经网络,用Lyapunov方法讨论平衡点的全局指数稳定性,给出了平衡点全局指数稳定的几个判别准则,作为特例,获得了连续型Hopfield神经网络全局指数稳定的新判据。     

具有时变时滞的递归神经网络的渐近稳定性分析

当神经网络应用于最优化计算时,理想的情形是只有一个全局渐近稳定的平衡点,并且以指数速度趋近于平衡点,从而减少神经网络所需计算时间.研究了带时变时滞的递归神经网络的全局渐近稳定性.首先将要研究的模型转化为描述系统模型,然后利用Lyapunov-Krasovskii稳定性定理、线性矩阵不等式(LMI)技术、S过程和代数不等式方法,得到了确保时变时滞递归神经网络渐近稳定性的新的充分条件,并将它应用于常时滞神经网络和时滞细胞神经网络模型,分别得到了相应的全局渐近稳定性条件.理论分析和数值模拟显示,所得结果为时滞递归神经网络提供了新的稳定性判定准则.     

An analysis of global asymptotic stability of delayed cellular neural networks

In this paper, a new sufficient condition is given for the uniqueness and global asymptotic stability of the equilibrium point for delayed cellular neural networks (DCNNs). This condition imposes constraints on the feedback and delayed feedback matrices of a DCNN independently of the delay parameter. This result is also compared with the previous results derived in the literature.     

Some Characterizations of Global Exponential Stability of a Generic Class of Continuous-Time Recurrent Neural Networks

This paper reveals two important characterizations of global exponential stability (GES) of a generic class of continuous-time recurrent neural networks. First, we show that GES of the neural networks can be fully characterized by global asymptotic stability (GAS) of the networks plus the condition that the maximum abscissa of spectral set of Jacobian matrix of the neural networks at the unique equilibrium point is less than zero. This result provides a very useful and direct way to distinguish GES from GAS for the neural networks. Second, we show that when the neural networks have small state feedback coefficients, the supremum of exponential convergence rates (ECRs) of trajectories of the neural networks is exactly equal to the absolute value of the maximum abscissa of spectral set of Jacobian matrix of the neural networks at the unique equilibrium point. Here, the supremum of ECRs indicates the potentially fastest speed of trajectory convergence. The obtained results are helpful in understanding the essence of GES and clarifying the difference between GES and GAS of the continuous-time recurrent neural networks.     

Global asymptotic stability of delay BAM neural networks with impulses via nonsmooth analysis

In this paper, we study global asymptotic stability of delay bi-directional associative memory (BAM) neural networks with impulses. We obtain a sufficient condition of ensuring existence and uniqueness of equilibrium point for delay BAM neural networks with impulses basing on nonsmooth analysis. And we give a criteria of global asymptotic stability of the unique equilibrium point for delay BAM neural networks with impulses using Lyapunov method. At last, we present examples to illustrate that our results are feasible.     

The globally asymptotic stability analysis for a class of recurrent neural networks with delays

This paper considers the problem of global stability of neural networks with delays. By combining Lie algebra and the Lyapunov function with the integral inequality technique, we analyze the globally asymptotic stability of a class of recurrent neural networks with delays and give an estimate of the exponential stability. A few new sufficient conditions and criteria are proposed to ensure globally asymptotic stability of the equilibrium point of the neural networks. A few simulation examples are presented to demonstrate the effectiveness of the results and to improve feasibility.     

Global asymptotic stability of high-order Hopfield type neural networks with time delays

This paper studies the problem of global asymptotic stability of a class of high-order Hopfield type neural networks with time delays. By utilizing Lyapunov functionals, we obtain some sufficient conditions for the global asymptotic stability of the equilibrium point of such neural networks in terms of linear matrix inequality (LMI). Numerical examples are given to illustrate the advantages of our approach.     

基于二次型的CNN全局渐近稳定性研究

细胞神经网络稳定性目前已经在图像处理、视频通信和最优控制等领域得到了一定的应用,因此进行稳定性的研究具有重要的意义,如何选择合理的参数模板是研究稳定性的关键问题。运用Lyapunov第二方法对细胞神经网络的全局渐近稳定性进行分析,通过构造出一个较好的Lyapunov函数来得到判定系统全局渐近稳定的一组新的充分条件。该条件改进了已有的结论,进一步推导和完善了系统全局渐近稳定平衡点为原点时的充分条件,经过数值仿真实验验证了其有效性和可行性。     

一类广义时变时滞神经网络的动态分析

讨论了一类广义时变时滞递归神经网络的平衡点的存在性、唯一性和全局指数稳定性。这个神经网络模型包括时滞Hopfield神经网络,时滞Cellular神经网络,时滞Cohen-Grossberg神经网络作为特例。基于微分不等式技术,利用Brouwer不动点定理并构造合适的Lyapunov函数,得到了保证递归神经网络的平衡点存在、唯一、全局指数稳定的新的充分条件。新的充分条件不要求激励函数的可微性、有界性和单调性,同时减少了对限制条件的要求。两个仿真例子表明了所得结果的有效性。     

Passivity Analysis of Dynamic Neural Networks with Different Time-scales

Dynamic neural networks with different time-scales include the aspects of fast and slow phenomenons. Some applications require that the equilibrium points of the designed networks are stable. In this paper, the passivity-based approach is used to derive stability conditions for dynamic neural networks with different time-scales. Several stability properties, such as passivity, asymptotic stability, input-to-state stability and bounded input bounded output stability, are guaranteed in certain senses. A numerical example is also given to demonstrate the effectiveness of the theoretical results.     

Impulsive Control for a Class of Cellular Neural Networks with Proportional Delay

This paper is concerned with a class of cellular neural networks with proportional delay and impulses. First, by employing the improved Razumikhin technique and Lyapunov functions, some delay-dependent criteria are established to guarantee asymptotic stability and global stability of a class of general impulsive differential equations with proportional delay. Second, applying the obtained criteria, we get some delay-dependent sufficient conditions ensuring the existence, uniqueness and globally asymptotic stability of the equilibrium point of the cellular neural networks with proportional delay and impulses presented in this paper. Finally, three examples are presented to illustrate the effectiveness and advantages of the results obtained.