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浙江大学学报(工学版)
J4  2009, Vol. 43 Issue (8): 1383-1388    DOI: 10.3785/j.issn.1008-973X
计算机科学技术     
离散时滞标准神经网络模型的鲁棒稳定性分析
张建海1，张森林2，刘妹琴2
(1. 杭州电子科技大学 计算机学院, 浙江 杭州 310018； 2 .浙江大学 电气工程学院, 浙江 杭州 310027)
Robust stability analysis of delayed discretetime standard neural network model
 ZHANG Jian-Hai1, ZHANG Sen-Lin2, LIU Mei-Qin2
1. College of Computer Science, Hangzhou Dianzi University, Hangzhou 310018, China;
2. College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China
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摘要：

研究了离散时滞标准神经网络模型（SNNM）的鲁棒渐进稳定性和指数稳定性问题,结合Lyapunov稳定性理论和S方法推导出了两种稳定性的充分条件.所得到的稳定性条件被表示为线性矩阵不等式形式,便于求解.特别的,将鲁棒指数稳定性问题转化为一个广义特征值问题,除了可以判断网络的指数稳定性,还可以方便地估计其最大指数收敛率.在数值示例中,将两类递归神经网络（RNNs）转化为SNNM的形式并利用得到的相关结论对其鲁棒稳定性进行了分析,仿真结果验证了稳定性判据的有效性.SNNM为分析递归网络提供了新的思路,简单且有效.
Abstract:

The problems of robust asymptotic stability and exponential stability of delayed discrete-time standard neural network model (SNNM) were investigated. Applying Lyapunov stability theory and S-procedure technique, sufficient stability conditions were derived in form of linear matrix inequalities, which could be solved easily. Especially, the condition for robust exponential stability was formulated as a generalized eigenvalued problem, which established an estimation of the exponential convergence rate and improved the previous results. In the given examples, two kinds of recurrent neural networks (RNNs) were transformed into SNNM to be analyzed in a unified way. Simulation showed the effectiveness of the presented method and the validity of the sufficient conditions. SNNM provides a new approach for the analysis of RNNs.
出版日期: 2009-09-28
:  TP 183  
基金资助:

国家自然科学基金资助项目（60801054，60874050）；浙江省自然科学基金资助项目（Y1080970）
通讯作者: 张森林，男，教授.     E-mail: slzhang@zju.edu.cn
作者简介: 张建海（1978-），男，山东潍坊人，博士，从事神经网络及非线性系统研究.
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引用本文:

张建海, 张森林, 刘妹琴. 离散时滞标准神经网络模型的鲁棒稳定性分析[J]. J4, 2009, 43(8): 1383-1388.

ZHANG Jian-Hai, ZHANG Sen-Lin, LIU Mei-Qin. Robust stability analysis of delayed discretetime standard neural network model. J4, 2009, 43(8): 1383-1388.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X    或    http://www.zjujournals.com/eng/CN/Y2009/V43/I8/1383

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