Skip to main content
SpringerLink
Log in

Dynamical Analysis of Neural Networks with Time-Varying Delays Using the LMI Approach

  • Conference paper
  • First Online:
Book cover Neural Information Processing (ICONIP 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9491))

Included in the following conference series:

  • 2660 Accesses

Abstract

This study is concerned with the delay-range-dependent stability analysis for neural networks with time-varying delay and Markovian jumping parameters. The time-varying delay is assumed to lie in an interval of lower and upper bounds. The Markovian jumping parameters are introduced in delayed neural networks, which are modeled in a continuous-time along with finite-state Markov chain. Moreover, the sufficient condition is derived in terms of linear matrix inequalities based on appropriate Lyapunov-Krasovskii functionals and stochastic stability theory, which guarantees the globally asymptotic stable condition in the mean square. Finally, a numerical example is provided to validate the effectiveness of the proposed conditions.

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 EPUB and 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

References

  1. Haykin, S.: Neural Networks: A Comprehensive Foundation. Prentice Hall, NJ (1998)

    MATH  Google Scholar 

  2. Cichocki, A., Unbehauen, R.: Neural Networks for Optimization and Signal Processing. Wiley, Chichester (1993)

    MATH  Google Scholar 

  3. Roska, T., Chua, L.O.: Cellular neural networks with nonlinear and delay-type template. Int. J. Circuit Theory Appl. 20, 469–481 (1992)

    Article  MATH  Google Scholar 

  4. Xu, S., Lam, J., Ho, D.W.C., Zou, Y.: Novel global asymptotic stability criteria for delayed cellular neural networks. IEEE Trans. Circuits Syst. II, Exp. Briefs 52, 349–353 (2005)

    Article  Google Scholar 

  5. He, Y., Wang, Q.G., Wu, M.: LMI-based stability criteria for neural networks with multiple time-varying delays. Physica D 212, 126–136 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. He, Y., Wu, M., She, J.H.: Delay-dependent exponential stability for delayed neural networks with time-varying delay. IEEE Trans. Circuits Syst. II, Exp. Briefs 53, 230–234 (2006)

    Article  Google Scholar 

  7. Hua, C.C., Long, C.N., Guan, X.P.: New results on stability analysis of neural networks with time-varying delays. Phys. Lett. A 352, 335–340 (2006)

    Article  MATH  Google Scholar 

  8. He, Y., Liu, G., Rees, D.: New delay-dependent stability criteria for neural networks with time-varying delay. IEEE Trans. Neural Netw. 18, 310–314 (2007)

    Article  Google Scholar 

  9. He, Y., Liu, G., Rees, D., Wu, M.: Stability analysis for neural networks with time-varying interval delay. IEEE Trans. Neural Netw. 18, 1850–1854 (2007)

    Article  Google Scholar 

  10. Li, C.D., Feng, G.: Delay-interval-dependent stability of recurrent neural networks with time-varying delay. Neurocomputing 72, 1179–1183 (2009)

    Article  Google Scholar 

  11. Singh, V.: A new criterion for global robust stability of interval delayed neural networks. J. Comput. Appl. Math. 221, 219–225 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Balasubramaniam, P., Lakshmanan, S., Theesar, S.: State estimation for Markovian jumping recurrent neural networks with interval time varying delays. Nonlinear Dyn. 60, 661–675 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  13. Tino, P., Cernansky, M., Benuskova, L.: Markovian architectural bias of recurrent neural netwoks. IEEE Trans. Neural Netw. 15, 6–15 (2004)

    Article  Google Scholar 

  14. Li, H., Chen, B., Zhou, Q., Lin, C.: Robust exponential stability for delayed uncertain Hopfield neural networks with Markovian jumping parameters. Phys. Lett. A 372, 4996–5003 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. Wang, Z., Liu, Y., Liu, X.: State estimation for jumping recurrent neural networks with discrete and distributed delays. Neural Netw. 22, 41–48 (2009)

    Article  Google Scholar 

  16. Boyd, S., El Ghaouli, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994)

    Book  Google Scholar 

  17. Zhang, D., Yu, L.: \(H_{\infty }\) filtering for linear neutral systems with mixed time-varying delays and nonlinear perturbations. J. Franklin Inst. 347, 1374–1390 (2010)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Intelligent Systems Research, Geelong Waurn Ponds Campus, Deakin University, Geelong, Australia

    Shanmugam Lakshmanan, C. P. Lim, Asim Bhatti & Saeid Nahavandi

  2. School of Applied and Biomedical Sciences, Federation University, Ballarat, Australia

    David Gao

Authors
  1. Shanmugam Lakshmanan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. P. Lim
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Asim Bhatti
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. David Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Saeid Nahavandi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shanmugam Lakshmanan .

Editor information

Editors and Affiliations

  1. University of Istanbul, Istanbul, Turkey

    Sabri Arik

  2. University at Qatar, Doha, Qatar

    Tingwen Huang

  3. Tunku Abdul Rahman University College, Kuala Lumpur, Malaysia

    Weng Kin Lai

  4. University of Science Technology, Wuhan, China

    Qingshan Liu

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Lakshmanan, S., Lim, C.P., Bhatti, A., Gao, D., Nahavandi, S. (2015). Dynamical Analysis of Neural Networks with Time-Varying Delays Using the LMI Approach. In: Arik, S., Huang, T., Lai, W., Liu, Q. (eds) Neural Information Processing. ICONIP 2015. Lecture Notes in Computer Science(), vol 9491. Springer, Cham. https://doi.org/10.1007/978-3-319-26555-1_34

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-26555-1_34

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26554-4

  • Online ISBN: 978-3-319-26555-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation