[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()

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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

Author(s):

Li Tao;  Fei Shumin;  Zhu Qing

School of Automation, Southeast University, Nanjing 210096, China

Keywords:

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

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.

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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