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Delay-Dependent and Delay-Independent Stability Conditions of Delayed Cellular Neural Networks

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Neural Information Processing (ICONIP 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4232))

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Abstract

By using the saturation linearity of the output functions of neurons in cellular neural networks, and by adopting the method of decomposing the state space to sub-regions, the mathematical equations of delayed cellular neural networks are rewritten to be the form of linear differential difference equations in the neighbourhood of each equilibrium, which is an interior point of some sub-region. Based on this linear form and by using the stability theory of linear differential difference equations and the tool of M-matrix, delay-dependent and delay-independent stability algebraic criteria are obtained. All results obtained in this paper need only to compute the eigenvalues of some matrices or to examine the matrices to be M-matrix or to verify some inequalities to be holden.

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Author information

Authors and Affiliations

  1. Zhongyuan University of Technology, Zhengzhou Henan, 450007, China

    Wudai Liao, Dongyun Wang & Yulin Xu

  2. Huazhong University of Science and Technology, Wuhan Hubei, 430074, China

    Xiaoxin Liao

Authors
  1. Wudai Liao
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  2. Dongyun Wang
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  3. Yulin Xu
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  4. Xiaoxin Liao
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Editor information

Editors and Affiliations

  1. Dept. of Computer Science and Engineering, The Chinese Univ. of Hong Kong, Shatin, N.T., Hong Kong

    Irwin King

  2. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China

    Jun Wang

  3. The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

    Lai-Wan Chan

  4. Department of Computer Science and Engineering & Center for Cognitive Science, The Ohio State University, OH 43210, Columbus

    DeLiang Wang

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© 2006 Springer-Verlag Berlin Heidelberg

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Liao, W., Wang, D., Xu, Y., Liao, X. (2006). Delay-Dependent and Delay-Independent Stability Conditions of Delayed Cellular Neural Networks. In: King, I., Wang, J., Chan, LW., Wang, D. (eds) Neural Information Processing. ICONIP 2006. Lecture Notes in Computer Science, vol 4232. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11893028_59

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  • DOI: https://doi.org/10.1007/11893028_59

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-46479-2

  • Online ISBN: 978-3-540-46480-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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