[1] Li Tao, Fei Shumin, Zhu Qing,. Exponential stability criteria on neural networkswith continuously distributed delays [J]. Journal of Southeast University (English Edition), 2007, 23 (4): 529-533. [doi:10.3969/j.issn.1003-7985.2007.04.011]

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Exponential stability criteria on neural networkswith continuously distributed delays()

具有连续分布时滞神经网络系统的指数稳定性准则

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

23

Issue:

2007 4

Page:

529-533

Research Field:

Automation

Publishing date:

2007-12-30

Info

Title:

Exponential stability criteria on neural networkswith continuously distributed delays

具有连续分布时滞神经网络系统的指数稳定性准则

Author(s):

Li Tao;  Fei Shumin;  Zhu Qing

School of Automation, Southeast University, Nanjing 210096, China

李涛;  费树岷;  朱清

东南大学自动化学院, 南京 210096

Keywords:

exponential stability;  neural networks;  free-weighting matrix;  continuously distributed delay;  linear matrix inequality

指数稳定性;  神经网络;  自由权矩阵;  连续分布时滞;  线性矩阵不等式

PACS:

TP183

DOI:

10.3969/j.issn.1003-7985.2007.04.011

Abstract:

The exponential stability of a class of neural networks with continuously distributed delays is investigated by employing a novel Lyapunov-Krasovskii functional.Through introducing some free-weighting matrices and the equivalent descriptor form, a delay-dependent stability criterion is established for the addressed systems.The condition is expressed in terms of a linear matrix inequality(LMI), and it can be checked by resorting to the LMI in the Matlab toolbox.In addition, the proposed stability criteria do not require the monotonicity of the activation functions and the derivative of a time-varying delay being less than 1, which generalize and improve earlier methods.Finally, numerical examples are given to show the effectiveness of the obtained methods.

考虑了一类具有时变和连续分布时滞神经网络系统的指数稳定性问题.通过引入Lyapunov-Krasovskii泛函、自由权矩阵和等价的描述系统形式, 针对所考虑的系统建立了一个时滞相关的指数稳定性准则.该准则以线性矩阵不等式的形式给出, 能够很容易地用Matlab工具箱LMI进行检验.此外, 所得到的结论不需要激励函数的单调性且变时滞的导函数只要有上界结论就可以成立, 这拓展和发展了现有的一些结论.最后通过2个数值例子说明了所得结论的有效性.

References:

[1] Chen Wenhua, Lu Xueming.Delay-dependent exponential stability of neural networks with variable delay:an LMI approach[J].IEEE Transactions on Circuits and Systems—Ⅱ:Express Briefs, 2006, 53(9):837-842.
[2] Ruan S, Filfil R.Dynamics of a two-neuron system with discrete and distributed delays[J].Physica D, 2004, 191(3/4):323-342.
[3] Wang Zidong, Liu Yurong, Liu Xiaohui.On global asymptotic stability of neural networks with discrete and distributed delays[J].Physics Letter A, 2005, 345(4/5):299-308.
[4] Park Ju H. On global stability criterion for neural networks with discrete and distributed delays[J].Chaos, Solitons and Fractals, 2006, 30(4):897-902.
[5] Park Ju H. On global stability criterion of neural networks with continuously distributed delays[J].Chaos, Solitons and Fractals, in press, available online at www.sciencedirect.com, 2006.
[6] Zhang Qiang, Wei Xiaopeng.Global exponential stability of Hopfield neural networks with continuously distributed delays[J].Physics Letters A, 2003, 315(6/7/8):431-436.
[7] Song Qiankun, Cao Jinde. Global exponential stability of bidirectional associative memory neural networks with distributed delays[J].Journal of Computational and Applied Mathematics, 2007, 202(2):266-279.
[8] Song Qiankun, Cao Jinde.Stability analysis of Cohen-Grossberg neural network with both time-varying and continuously distributed delays[J].Journal of Computational and Applied Mathematics, 2006, 197(1):188-203.

Memo

Memo:

Biographies: Li Tao(1979—), male, graduate;Fei Shumin(corresponding author), male, doctor, professor, smfei@seu.edu.cn.

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