| 广义Hopfield神经网络的绝对指数稳定性 |
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| 引用本文： | 文海霞,黄丽湘,张继业.广义Hopfield神经网络的绝对指数稳定性[J].西南交通大学学报,2007,42(5):583-588. |
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| 作者姓名： | 文海霞 黄丽湘 张继业 |
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| 作者单位： | 1. 西南交通大学牵引动力国家重点实验室,四川,成都,610031;长沙理工大学桥梁与结构工程学院,湖南,长沙,410076
2. 西南交通大学牵引动力国家重点实验室,四川,成都,610031 |
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| 基金项目： | 新世纪优秀人才支持计划项目(NCET-04-0889)，四川省青年科技基金项目(05ZQ026-015) |
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| 摘 要： | 研究了一类广义神经网络系统平衡点的存在性、唯一性和绝对指数稳定性.这类神经网络包含Hopfield神经网络和细胞型神经网络,不要求激活函数可微和有界.应用拓扑理论,得到了广义Hopfield神经网络平衡点的存在性和唯一性的充分必要条件;利用矩阵的性质,通过构造Lurie型Liapunov函数,得到了广义Hopfield神经网络绝对指数稳定的充分条件以及几类特殊神经网络绝对指数稳定的充分必要条件.
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| 关 键 词： | 神经网络 绝对稳定性 指数稳定性 充分必要条件 |
| 文章编号： | 0258-2724（2007）05-0583-06 |
| 修稿时间： | 2006-12-08 |
Absolute Exponential Stability of Generalized Hopfield Neural Networks |
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| WEN Haixia,HUANG Lixiang,ZHANG Jiye.Absolute Exponential Stability of Generalized Hopfield Neural Networks[J].Journal of Southwest Jiaotong University,2007,42(5):583-588. |
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| Authors: | WEN Haixia HUANG Lixiang ZHANG Jiye |
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| Institution: | 1. Traction Power State Key Laboratory, Southwest Jiaotong University, Chengdu 610031, China; 2. School of Bridge and Structure Eng. , Changsha University of Science and Technology, Changsha 410076, China |
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| Abstract: | The existence and uniqueness of the equilibrium point of a class of generalized Hopfield neural networks(GHNN),altogether with its absolute exponential stability,were investigated.GHNN includes Hopfield neural networks and cellular neural networks,and it is not necessary for its activation functions to be differential and bounded functions.By applying the topology theory,the necessary and sufficient condition for the existence and uniqueness of the equilibrium point of GHNN was obtained.Based on matrix properties,the sufficient conditions for the absolute exponential stability of GHNN were given by constructing Lurie-type Liapunov functions.In some special cases,the necessary and sufficient conditions of the absolute exponential stability of neural networks were determined. |
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| Keywords: | neural network absolute stability exponential asymptotic stability necessary and sufficient condition |
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