Skip to main content
SpringerLink
Log in

A New LMI-Based Stability Criteria for Delayed Cellular Neural Networks

  • Conference paper
Advances in Neural Networks – ISNN 2009 (ISNN 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5551))

Included in the following conference series:

  • 1472 Accesses

Abstract

In this paper, the global asymptotic stability for delayed cellular neural networks is addressed with a new Lyapunov-Krasovskii function. New delay-independent LMI-based conditions for global asymptotic stability are derived. A key feature of the new approach is the introduction an integral of term of neuron activation functions in the Lyapunov-Krasovskill function, which can provide useful and less conservative results. Finally, two numerical examples show the effectiveness of the proposed method.

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 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
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. Chua, L., Yang, L.: Cellular Neural Networks: Theory. IEEE Trans. Circuits Syst. 35, 1257–1272 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  2. Cao, J., Zhou, D.: Stability Analysis of Delayed Cellular Neural Nwtworks. Neural Netw. 11, 1601–1605 (1998)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  4. Liao, T., Wang, F.: Global Stability of Cellular Neural Networks with Time Delay. IEEE Trans. on Neural Netw. 11, 1481–1484 (2000)

    Article  Google Scholar 

  5. Cao, J.: Global Stability Conditions for Delayed CNNs. IEEE Trans Circuits Syst. I. 48, 1330–1333 (2001)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. Arik, S.: An Analysis of Global Asymptotic Stability of Delayed Cellular Neural Networks. IEEE Trans. Neural Netw. 13, 1239–1242 (2002)

    Article  Google Scholar 

  8. Ensari, T., Arik, S.: Global Stability Analysis of Neural Networks with Multiple Time Varying Delays. IEEE Trans. Automat. Control 50, 1781–1785 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Xu, S., Lam, J., Ho, D., Zou, Y.: Novel Global Asymptotic Stability Criteria for Delayed Cellular Neural Networks. IEEE Trans. Circuits Syst. II 52, 349–353 (2005)

    Article  Google Scholar 

  10. Liao, X., Chen, G., Sanchez, E.N.: Delay-Dependent Exponential Stability Analysis of Delayed Neural Networks: an LMI Approach. Neural Netw. 15, 855–866 (2002)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  12. He, Y., Wu, M., She, J.H.: Delay-Dependent Exponential Stability of Delayed Neural Networks with Time-Varying Delay. IEEE Trans. Circuit Syst. II 53, 553–557 (2006)

    Article  Google Scholar 

  13. Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadlephia (1994)

    Book  MATH  Google Scholar 

  14. Singh, V.: A Generalized Lmi-Based Approach to the Global Asymptotic Stability of Delayed Cellular Neural Networks. IEEE Trans. Neural Netw. 15, 223–225 (2004)

    Article  Google Scholar 

  15. Zhang, H., Li, C., Liao, X.: A Note on the Robust Stability of Neural Networks with Time Delay. Chaos, Solitons and Fractals 25, 357–360 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  16. Cao, J., Ho, D.: A General Framework for Global Asymptotic Stability of Delayed Neural Networks Based on LMI Approach. Chaos, Solitons and Fractals 24, 1317–1329 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  17. Singh, V.: Simplified LMI Condition for Global Asymptotic Stability of Delayed Neural Networks. Chaos, Solitons and Fractals 29, 470–473 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  18. He, Y., Wu, M., She, J.: An Improved Global Asymptotic Stability Criterion for Delayed Cellular Neural Networks. IEEE Trans. Neural Netw. 17, 250–252 (2006)

    Article  Google Scholar 

  19. Shen, Y.: LMI-based Stability Criteria with Auxiliary Matrices for Delayed Recurrent Neural Networks. IEEE Transaction on Circuits System II 55, 811–815 (2008)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Science, China Three Gorges University, Yichang, Hubei, 443002, China

    Yanjun Shen & Yong Zhang

  2. Hubei Three Gorges Vocation and Technology College, Yichang, Hubei, 443000, China

    Linguo Zhang

Authors
  1. Yanjun Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Linguo Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yong Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Departamento de Control Automático, CINVESTAV-IPN, A.P. 14-740, Av.IPN 2508, 07360, México D.F., México

    Wen Yu

  2. Deptartment of Electrical and Computer Engineering, Stevens Institute of Technology, NJ 07030, Hoboken, USA

    Haibo He

  3. Dept. of Electrical and Computer Engineering, South Dakota School of Mines & Technology, 501 E. St. Joseph Street, Rapid City, SD 57701, USA

    Nian Zhang

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Shen, Y., Zhang, L., Zhang, Y. (2009). A New LMI-Based Stability Criteria for Delayed Cellular Neural Networks. In: Yu, W., He, H., Zhang, N. (eds) Advances in Neural Networks – ISNN 2009. ISNN 2009. Lecture Notes in Computer Science, vol 5551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01507-6_41

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-01507-6_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-01506-9

  • Online ISBN: 978-3-642-01507-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation