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An LMI-Based Approach to the Global Stability of Bidirectional Associative Memory Neural Networks with Variable Delay

  • Minghui Jiang
  • Yi Shen
  • Xiaoxin Liao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3971)

Abstract

Based on the linear matrix inequality (LMI), new sufficient conditions on the global exponential stability and asymptotic stability of bidirectional associative memory neural networks with variable delay are presented, and exponential converging velocity index is estimated. Furthermore, the results in this paper are less conservative than the ones reported so far in the literature. One example is given to illustrate the feasibility of our main results.

Keywords

Neural Network Asymptotic Stability Linear Matrix Inequality Global Stability Recurrent Neural Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Kosko, B.: Bidirectional Associative Memories Systems. IEEE Trans. Man and Cybernetics 18, 49–60 (1988)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Cao, J., Wang, J.: Global Asymptotic Stability of Recurrent Neural Networks with Lipschitz-continuous Activation Functions and Time-Varying Delays. IEEE Trans. Circuits Syst. I 50, 34–44 (2003)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Zeng, Z., Wang, J., Liao, X.: Global Exponential Stability of a General Class of Recurrent Neural Networks with Time-Varying Delays. IEEE Trans. Circuits Syst. 50, 1353–1359 (2003)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Singh, V.: A Generalized LMI-Based Approach to the Global Asymptotic Stability of Delayed Cellular Neural Networks. IEEE Trans. Neural Networks 15, 223–225 (2004)CrossRefGoogle Scholar
  5. 5.
    Arik, S.: An Analysis of Global Asymptotic Stability of Delayed Cellular Neural Networks. IEEE Trans. Neural Networks 13, 1239–1242 (2002)CrossRefGoogle Scholar
  6. 6.
    Liao, T., Wang, F.: Global Stability for Cellular Neural Networks with Time Delay. IEEE Trans. Neural Networks 11, 1481–1484 (2000)CrossRefGoogle Scholar
  7. 7.
    Zhao, H.: Global Stability of Bidirectional Associative Memory Neural Networks with Distributed Delays. Phys. Lett. A 30, 519–546 (2002)Google Scholar
  8. 8.
    Arik, S., Tavsanoglu, V.: Global Asymptotic Stability Analysis of Bidirectional Associative Memory Neural Networks with Constant Time Delays. Neurocomputing 68, 161–176 (2005)CrossRefGoogle Scholar
  9. 9.
    Liao, X., Yu, J.: Qualitative Analysis of Bi-directional Associative Memory with Time Delay. Int. J. Circuit Theory Appl. 26, 219–229 (1998)MATHCrossRefGoogle Scholar
  10. 10.
    Liao, X., Yu, J., Chen, G.: Novel Stability Criteria for Bidirectional Associative Memory Neural Networks with Time Delays. Int. J. Circuit Theory Appl. 30, 519–546 (2002)MATHCrossRefGoogle Scholar
  11. 11.
    Mohamad, S.: Global Exponential Stability in Continuous-time and Discrete-time Delayed Bidirectional Neural Networks. Physica D 159, 233–251 (2001)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Yi, Z., Tan, K.K.: Convergence Analysis of Recurrent Neural Networks. Kluwer Academic Publishers, Dordrecht (2003)Google Scholar
  13. 13.
    Chen, M., Chen, Z., Chen, G.: Approximate Solution of Operation Equations. World Scientific, Singapore (1997)Google Scholar
  14. 14.
    Driver, R.D.: Ordinary and Delay Differential Equations. Springer, NewYork (1977)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Minghui Jiang
    • 1
  • Yi Shen
    • 2
  • Xiaoxin Liao
    • 2
  1. 1.Institute of Nonlinear Complex SystemsThree Gorges UniversityYichangChina
  2. 2.Department of Control Science and EngineeringHuazhong University of Science and TechnologyWuhanChina

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