动态分布参数神经网络时空稳定性分析

本文将Hopfield自联想神经网络和Kosko异联想神经网络推广到无穷维状态空间动态神经网络,即动态分布参数神经网络,并给出了它们的有界性和稳定性。尤其是还研究了带微分算子的多维分布参数神经网络的时空稳定性以及保证稳定情况下所应满足的边界条件。最后,还给出了一个应用实例。     

Global asymptotic stability and global exponential stability of neural networks with unbounded time-varying delays

This brief studies the global asymptotic stability and the global exponential stability of neural networks with unbounded time-varying delays and with bounded and Lipschitz continuous activation functions. Several sufficient conditions for the global exponential stability and global asymptotic stability of such neural networks are derived. The new results given in the brief extend the existing relevant stability results in the literature to cover more general neural networks.     

Global exponential stability and periodicity of recurrent neural networks with time delays

In this paper, the global exponential stability and periodicity of a class of recurrent neural networks with time delays are addressed by using Lyapunov functional method and inequality techniques. The delayed neural network includes the well-known Hopfield neural networks, cellular neural networks, and bidirectional associative memory networks as its special cases. New criteria are found to ascertain the global exponential stability and periodicity of the recurrent neural networks with time delays, and are also shown to be different from and improve upon existing ones.     

Stability Analysis of Delay Neural Networks With Impulsive Effects

A generalized model of neural networks with time-varying delays and impulsive effects is considered. By establishing an impulsive delay differential inequality, we investigate the global exponential stability and uniform stability of impulsive delay neural networks. Our sufficient conditions ensuring the stability are dependent on delays and impulses and show delay and impulsive effects on the stability of neural networks. The results extend and improve the earlier publications.     

Sufficient and necessary conditions for global exponential stability of discrete-time recurrent neural networks

A set of sufficient and necessary conditions are presented for global exponential stability (GES) of a class of generic discrete-time recurrent neural networks. By means of the uncovered conditions, GES and convergence properties of the neural networks are analyzed quantitatively. It is shown that exact equivalences exist among the GES property of the neural networks, the contractiveness of the deduced nonlinear operators, and the global asymptotic stability (GAS) of the neural networks plus the spectral radius of Jacobian matrix of the neural networks at the unique equilibrium point less than one. When the neural networks have small state feedback coefficients, it is shown further that the infimum of exponential bounds of the trajectories of the neural networks equals exactly the spectral radius of Jacobian matrix of the neural networks at the unique equilibrium point. The obtained results are helpful in understanding essence of GES and clarifying difference between GES and GAS of the discrete-time recurrent neural networks.     

STABILITY CONTROL AND ANALYSIS OF ASYMMETRIC CONTINUOUS NEURAL NETWORKS

A new method for analyzing dynamics of continuous neural networks is proposed,and the necessary convergence conditions for a class of associative networks are obtained. Basedon the stability criterion and the equations of equilibrium set of the network, synthesis of aclass of associative neural networks is given. The stability control model of asymmetric unstablenetworks is suggested, which is also a valid way for optimization and dynamic control of stableneural networks.     

多时滞神经网络的全局指数稳定性

多时滞神经网络是一种特殊结构的动力系统,其全局指数稳定性在实际应用中起着非常重要的作用.本文通过构建Lyapunov函数的方法,对一类一般多时滞神经网络的全局指数稳定进行了分析,得到了多时滞神经网络全局指数稳定性的几个充分条件,本文的结果涵盖并推广了最近文献的结论,并给出实例进行数字仿真说明本文结果的有效性.     

Global asymptotic stability of a class of feedback neural networks with an application to optimization problems

By applying results from homotopy theory, new conditions are obtained for the existence and uniqueness of an equilibrium for a class of continuous-time feedback neural networks which contains the Hopfield model as a special case. Next, new criteria are established for the global asymptotic stability of the unique equilibrium of this class of neural networks by utilizing Lur'e-type Lyapunov functions and the stability theory for systems of differential inequalities. Several practical stability testing conditions are given. As a special case, criteria are derived for the global asymptotic stability of Hopfield neural networks. This is followed by a robustness analysis of the class of neural networks considered. The results obtained are then applied to an optimization problem.This work was supported in part by the National Science Foundation under Grant ECS 93-19352.     

随机细胞神经网络的指数稳定性

本文研究了随机时滞细胞神经网络的指数稳定性,建立了这种细胞神经网络均方指数稳定与几乎必然指数稳定的充分条件,其条件分为时滞无关与时滞相关两种.     

Global asymptotic and robust stability of recurrent neural networks with time delays

In this paper, two related problems, global asymptotic stability (GAS) and global robust stability (GRS) of neural networks with time delays, are studied. First, GAS of delayed neural networks is discussed based on Lyapunov method and linear matrix inequality. New criteria are given to ascertain the GAS of delayed neural networks. In the designs and applications of neural networks, it is necessary to consider the deviation effects of bounded perturbations of network parameters. In this case, a delayed neural network must be formulated as a interval neural network model. Several sufficient conditions are derived for the existence, uniqueness, and GRS of equilibria for interval neural networks with time delays by use of a new Lyapunov function and matrix inequality. These results are less restrictive than those given in the earlier references.     

细胞神经网络的全局指数稳定性

本文研究了细胞神经网络的全局指数稳定性问题,运用Lyapunov函数法和不等式的分析技巧给出了细胞神经网络全局指数稳定的三个判据。     

Robust Stability and Robust Periodicity of Delayed Recurrent Neural Networks With Noise Disturbance

Neural networks suffer from the natural intra- and inter-cellular noise perturbations and environmental fluctuations. Such noises will undoubtedly affect the dynamics of the neural networks both quantitatively and qualitatively. In this paper, we study the effects of noise perturbations on the stability and periodicity of delayed recurrent neural networks. We first derive the mean-square stability conditions for stochastic delayed recurrent neural networks without and with parametric uncertainties, respectively. After that, we study the stochastic periodicity (stability) with disturbance attenuation of delayed recurrent neural networks. The analysis are all based on the Lyapunov–Krasovskii functional approach, and the conditions are all expressed in terms of linear matrix inequalities, which can be easily solved by using the effective convex optimization techniques. Several numerical examples are also given to demonstrate the correctness and effectiveness of the theoretical results.     

Global robust stability of a class of discrete-time interval neural networks

This paper is concerned with global robust stability of a general class of discrete-time interval neural networks which contain time-invariant uncertain parameters with their values being unknown but bounded in given compact sets. We first introduce the concept of diagonally constrained interval neural networks and present a necessary and sufficient condition for global robust stability of the interval networks regardless of the bounds of nondiagonal uncertain parameters of state feedback and connection weight matrices. Then we extend the result to general interval neural networks. Finally, simulation results illustrate the characteristics of the main results.     

Global asymptotic stability of a class of neural networks with distributed delays

In this paper, the problem of stability analysis for a class of neural networks with distributed delays is investigated. Applying the M-matrix theory and new analysis technique, novel sufficient conditions for the existence, uniqueness, and global asymptotic stability of the equilibrium point of neural networks with distributed delays are derived. The new stability criteria can be applied to the case when the nondelayed terms cannot dominate the delayed terms, which have great significance in the design and application of neural networks with distributed delays. Three illustrative examples are presented which demonstrate the usefulness of the proposed results.     

高阶Hopfield型神经网络的定性分析

本文讨论高阶连续型Hopfield神经网络平衡态的性质,包括平衡态的存在唯一性和稳定性.借助于Banach不动点原理和Lyapunov方法得到了若干平稳态存在唯一和全局渐近稳定的充分条件.作为特例,获得了一阶连续型Hopfield神经网络稳定性的新判据.     

NLq theory: checking and imposing stability of recurrentneural networks for nonlinear modeling

It is known that many discrete-time recurrent neural networks, such as e.g., neural state space models, multilayer Hopfield networks, and locally recurrent globally feedforward neural networks, can be represented as NL_q systems. Sufficient conditions for global asymptotic stability and input/output stability of NL_q systems are available, including three types of criteria: (1) diagonal scaling; (2) criteria depending on diagonal dominance; (3) condition number factors of certain matrices. The paper discusses how Narendra's (1990, 1991) dynamic backpropagation procedure, which is used for identifying recurrent neural networks from I/O measurements, can be modified with an NL_q stability constraint in order to ensure globally asymptotically stable identified models. An example illustrates how system identification of an internally stable model corrupted by process noise may lead to unwanted limit cycle behavior and how this problem can be avoided by adding the stability constraint     

On Stability of Neural Networks by a Lyapunov Functional-Based Approach

In this paper, a new Lyapunov functional-based method is proposed for the stability analysis of delayed cellular neural networks (DCNN). Global exponential stability conditions are obtained for the general DCNN, the Hopfield neural networks (HNNs), and delayed HNNs with monotonic nondecreasing and nonconstant activation functions     

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。     

时延不对称Hopfield神经网络的稳定条件及其应用

本文对具有时延的不对称Hopfield型神经网络平衡点的稳定性进行了分析,得到了网络平衡点全局渐近稳定的一些充分条件,最后我们说明了分析结果在网络设计和参数选择中的应用。