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Global Exponential Stability of Fuzzy Cellular Neural Networks with Variable Delays

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Advances in Neural Networks - ISNN 2006 (ISNN 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3971))

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Abstract

In this paper, the global exponential stability of fuzzy cellular neural networks with time-varying delays is studied. Without assuming the boundedness and differentiability of the activation functions, based on the properties of M-matrix, by constructing vector Liapunov functions and applying differential inequalities, the sufficient conditions ensuring existence, uniqueness, and global exponential stability of the equilibrium point of fuzzy cellular neural networks with variable delays are obtained.

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References

  1. Chua, L.O., Yang, L.: Cellular Neural Networks: Theory. IEEE Trans. Circ. Syst. 35, 1257–1272 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  2. Arik, S., Tavsanoglu, V.: On the Global Asymptotic Stability of Delayed Cellular Neural Networks. IEEE Trans. Circ. Syst.- I 47, 571–574 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  3. Arik, S.: An Improved Global Stability Result for Delayed Cellular Neural Networks. IEEE Trans. Circ. Syst. 49, 1211–1214 (2002)

    Article  MathSciNet  Google Scholar 

  4. Gopalsamy, K., He, X.: Stability in Asymmetric Hopfield Nets with Transmission Delays. Physica D 76, 344–358 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  5. Forti, M., Tesi, A.: New Conditions for Global Stability of Neural Networks with Application to Linear and Quadratic Programming Problems. IEEE Trans. Circ. Syst.-I 42, 354–366 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  6. Yang, T., Yang, L.B.: Exponential Stability of Fuzzy Cellular Neural Networks with Constant and Time-Varying Delays. IEEE Trans. Circ. Syst.-I 43, 880–883 (1996)

    Article  Google Scholar 

  7. Yang, T., Yang, L.B.: Fuzzy Cellular Neural Networks: A New Paradigm for Image Processing. Int. J. Circ. Theor. Appl. 25, 469–481 (1997)

    Article  Google Scholar 

  8. Roska, T., Wu, C.W., Balsi, M., Chua, L.O.: Stability of Cellular Neural Networks with Dominant Nonlinear and Delay-Type Templates. IEEE Trans. Circ. Syst. 40, 270–272 (1993)

    Article  MATH  Google Scholar 

  9. Zhang, J.: Global Stability Analysis in Delayed Cellular Neural Networks. Computers and Mathematics with Applications 45, 1707–1720 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  10. Zhang, J.: Absolutely Exponential Stability in Delayed Cellular Neural Networks. Int. J. Circ. Theor. Appl. 30, 395–409 (2002)

    Article  MATH  Google Scholar 

  11. Zhang, J.: Globally Exponential Stability of Neural Networks with Variable Delays. IEEE Trans. Circ. Syst.-I 50, 288–291 (2003)

    Article  Google Scholar 

  12. Yucel, E., Arik, S.: New Exponential Stability Results for Delayed Neural Networks with Time Varying Delays. Physica D 191, 314–322 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  13. Zhang, J.: Absolute Stability Analysis in Cellular Neural Networks with Variable Delays and Unbounded Delay. Computers and Mathematics with Applications 47, 183–194 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  14. Van Den Driessche, P., Zou, X.: Global Attractivity in Delayed Hopfield Neural Networks Models. SIAM J. Appl. Math. 58, 1878–1890 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  15. Chen, T.: Global Exponential Stability of Delayed Hopfield Neural Networks. Neural Networks 14, 977–980 (2001)

    Article  Google Scholar 

  16. Xu, D., Zhao, H., Zhu, H.: Global Dynamics of Hopfield Neural Networks Involving Variable Delays. Computers and Mathematics with Applications 42, 39–45 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  17. Zhang, J., Suda, Y., Iwasa, T.: Absolutely Exponential Stability of a Class of Neural Networks with Unbounded Delay. Neural Networks 17, 391–397 (2004)

    Article  MATH  Google Scholar 

  18. Liu, Y., Tang, W.: Exponential Stability of Fuzzy Cellular Neural Networks with Constant and Time-Varying Delays. Physics Letters A 323, 224–233 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  19. Siljak, D.D.: Large-Scale Dynamic Systems-Stability and Structure. Elsevier, New York (1978)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Traction Power State Key Laboratory, Southwest Jiaotong University, Chengdu, 610031, China

    Jiye Zhang, Dianbo Ren & Weihua Zhang

Authors
  1. Jiye Zhang
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  2. Dianbo Ren
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  3. Weihua Zhang
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Editor information

Editors and Affiliations

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

    Jun Wang

  2. Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, 610054, Chengdu, P.R. China

    Zhang Yi

  3. Department of Electrical Engineering, University of Louisville, 40292, Louisville, KY, U.S.A

    Jacek M. Zurada

  4. Laboratory for Computational Biology, Shanghai Center for Systems Biomedicine, 800 Dong Chuan Rd., 200240, Shanghai, China

    Bao-Liang Lu

  5. School of Electrical and Electronic Engineering, University of Manchester, UK

    Hujun Yin

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© 2006 Springer-Verlag Berlin Heidelberg

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Zhang, J., Ren, D., Zhang, W. (2006). Global Exponential Stability of Fuzzy Cellular Neural Networks with Variable Delays. In: Wang, J., Yi, Z., Zurada, J.M., Lu, BL., Yin, H. (eds) Advances in Neural Networks - ISNN 2006. ISNN 2006. Lecture Notes in Computer Science, vol 3971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11759966_36

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  • DOI: https://doi.org/10.1007/11759966_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34439-1

  • Online ISBN: 978-3-540-34440-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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