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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (4): 608-622.doi: 10.3969/j.issn.1005-3085.2015.04.014

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时滞脉冲周期细胞神经网络指数稳定性的平均准则(英)

宋学力,   赵  盼,   王小伟   

  1. 长安大学理学院，西安 710064
  • 收稿日期:2014-10-15 接受日期:2015-04-23 出版日期:2015-08-15 发布日期:2015-10-15
  • 基金资助:
    国家自然科学基金 (11201038)；陕西省青年科技新星计划 (2014KJXX-55)；长安大学中央高校基础科学研究专项资金 (2013G2121017).

An Average Criterion for Global Exponential Stability of Periodic CNNs with Delay and Impulses

SONG Xue-li,   ZHAO Pan,   WANG Xiao-wei   

  1. School of Science, Chang'an University, Xi'an 710064
  • Received:2014-10-15 Accepted:2015-04-23 Online:2015-08-15 Published:2015-10-15
  • Supported by:
    The National Natural Science Foundation of China (11201038); the Youth Science and Technology Nova Program of Shaanxi Province (2014KJXX-55); the Special Fund for Basic Scientific Research of Central Colleges in Chang'an University (2013G2121017).

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摘要： 本文致力于研究具有周期系数的脉冲时滞非自治细胞神经网络的全局指数稳定性．具体地，利用非线性测度方法和周期Halanay微分不等式，我们获得了该类神经网络的积分平均意义下的稳定性准则．我们的方法不要求激活函数的有界性和单调性，这意味着我们的稳定性准则和现有的某些结果相比受到的约束限制少，可以被应用到更一般的实际问题．此外，我们获得的稳定性准则是现有某些研究结果的推广和改进．最后，文中的例子说明了我们的方法是有效的，获得的结果是正确的．

关键词: 全局指数稳定性, 细胞神经网络, 周期Halanay微分不等式, 非线性测度

Abstract:

This paper investigates the global exponential stability of non-autonomous impulsive and delayed cellular neural networks with periodic coefficients. Particularly, by means of the nonlinear measure method and periodic Halanay differential inequality, we obtain an integral average criterion for global exponential stability of this class of neural networks. Our method does not require assumptions on boundedness and monotonicity of activation functions, which demonstrates that our derived criterion is less restrictive than some existing ones and can be applied to more general practical problems. Moreover, our stability criterion is the generalization and improvement of some existing ones. Finally, an example illustrates the effectiveness of our method and the correctness of our results.

Key words: global exponential stability, cellular neural networks, periodic Halanay differential inequality, nonlinear measure

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