Skip to main content
SpringerLink
Log in

Global Stability of a Class of High-Order Recurrent Neural Networks with Multiple Delays

  • Conference paper
Advances in Brain Inspired Cognitive Systems (BICS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7366))

Included in the following conference series:

  • 1749 Accesses

Abstract

Global asymptotic stability problem for a general class of higher order recurrent neural networks (HRNN) with multiple delays has been studied based on delay-matrix decomposition method and linear matrix inequality (LMI) technique. The proposed stability criterion is suitable for a general class of multiple delayed higher order recurrent Neural Networks. Especially, for this system, we have also established corresponding LMI-based stability criteria which are simple in expression form and easy to check to deal with the different multiple delays. Compared with the existing results, our results are new and can be regarded as an alternative of M-matrix based stability results in the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Zeng, Z., Wang, J., Liao, X.: Global exponential stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans. Circuits and Systems-I: Fundamental Theory and Applications 50, 1353–1358 (2003)

    Article  MathSciNet  Google Scholar 

  2. Zhang, H., Wang, Z.: Global asymptotic stability of delayed cellular neural networks. IEEE Trans. Neural Networks 18, 947–950 (2007)

    Article  Google Scholar 

  3. Zhang, H., Wang, Z., Liu, D.: Global asymptotic stability of recurrent neural networks with multiple time varying delays. IEEE Trans. Neural Networks 19, 855–873 (2008)

    Article  Google Scholar 

  4. Zhang, H., Wang, Z., Liu, D.: Robust stability analysis for interval cohen-grossberg neural network with unknown time-varying delays. IEEE Trans. Neural Networks 19, 1942–1955 (2008)

    Article  Google Scholar 

  5. Ziegaus, C., Lang, E.: A neural implementation ofthe JADE algorithm (nJADE) using higher-order neurons. Neurocomputing 56, 79–100 (2004)

    Article  Google Scholar 

  6. Xu, B., Liu, X., Liao, X.: Stability analysis of high-order Hopfield type neural networks with uncertainty. Neurocomputing 71, 508–512 (2008)

    Article  Google Scholar 

  7. Xu, B., Wang, Q., Liao, X.: Global exponential stability of high order Hopfield type neural networks. Appl. Math. Comput. 174, 98–116 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Qiu, J.: Dynamics of high-order Hopfield neural networks with time delays. Neurocomputing 73, 820–826 (2010)

    Article  Google Scholar 

  9. Cao, J., Liang, J., Lam, J.: Exponential stability of high-order bidirectional associative memory neural networks with time delays. Physica D 199, 425–436 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Huo, H., Li, W., Tang, S.: Dynamics of high-order BAM neural networks with and without impulses. Applied Mathematics and Computation 215, 2120–2133 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Hu, H., Jiang, H., Teng, Z.: The boundedness of high-order Hopfield neural networks with variable delays. Neurocomputing 73, 2589–2596 (2010)

    Article  Google Scholar 

  12. Ou, C.: Anti-periodic solutions for high-order Hopfield neural networks. Computers and Mathematics with Applications 56, 1838–1844 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Chen, T., Lu, W.: Stability analysis of dynamical neural networks. In: IEEE Int. Conf. Neural Networks and Signal Processing, Nanjing, China, December 14-17 (2003)

    Google Scholar 

  14. Chen, T.: Universal Approach to Study Delayed Dynamical Systems. In: Wang, L., Chen, K., S. Ong, Y. (eds.) ICNC 2005, Part I. LNCS, vol. 3610, pp. 245–253. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  15. Liu, P., Yi, F., Guo, Q., Yang, J., Wu, W.: Analysison global exponential robust stability of reactioncdiffusion neural networks with s-type distributed delays. Physica D 237, 475–485 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Wang, L., Xu, D.: Global asymptotic stability of bidirectional associative memory neural networks with s-type distributed delays. Internat. J. Syst. Sci. 33, 869–877 (2002)

    Article  MATH  Google Scholar 

  17. Wang, Z., Zhang, H., Liu, D., Feng, J.: LMI Based Global Asymptotic Stability Criterion for Recurrent Neural Networks with Infinite Distributed Delays. In: Yu, W., He, H., Zhang, N. (eds.) ISNN 2009, Part I. LNCS, vol. 5551, pp. 463–471. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  18. Chen, T.: Universal Approach to Study Delayed Dynamical Systems. In: Wang, L., Chen, K., S. Ong, Y. (eds.) ICNC 2005, Part I. LNCS, vol. 3610, pp. 245–253. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  19. Chen, T.: Universal approach to study delayed dynamical systems. SCI, vol. 35, pp. 85–110 (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, 110004, People’s Republic of China

    Zhanshan Wang & Yongbin Zhao

  2. College of Engineering, Bohai University, Jinzhou, 121000, People’s Republic of China

    Shuxian Lun

Authors
  1. Zhanshan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yongbin Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shuxian Lun
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. College of Information Science and Engineering, Northeastern University, 110004, Shenyang, P.R. China

    Huaguang Zhang

  2. Dept. of Computing Science and Mathematics, University of Stirling, FK9 4LA, Stirling, Scotland, UK

    Amir Hussain

  3. Institute of Automation, Chinese Academy of Sciences, 100190, Beijing, China

    Derong Liu

  4. Northeastern University, School of Information Science and Engineering, 110004, Shenyang, Liaoning, People’s Republic of China

    Zhanshan Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wang, Z., Zhao, Y., Lun, S. (2012). Global Stability of a Class of High-Order Recurrent Neural Networks with Multiple Delays. In: Zhang, H., Hussain, A., Liu, D., Wang, Z. (eds) Advances in Brain Inspired Cognitive Systems. BICS 2012. Lecture Notes in Computer Science(), vol 7366. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31561-9_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31561-9_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31560-2

  • Online ISBN: 978-3-642-31561-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation