Skip to main content
SpringerLink
Log in

Asymptotic Stability Criterion for Fuzzy Recurrent Neural Networks with Interval Time-Varying Delay

  • Conference paper
Mathematical Modelling and Scientific Computation (ICMMSC 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 283))

  • 1715 Accesses

Abstract

This paper focuses on the delay-dependent asymptotic stability for fuzzy recurrent neural networks (FRNNs) with interval time-varying delay. The delay interval is decomposed into multiple uniform subintervals, Lyapunov-Krasovskii functionals (LKFs) are constructed on these intervals. By employing these LKFs, new delay-dependent asymptotic stability criterion is proposed in terms of Linear Matrix Inequalities (LMIs), which can be easily solved by MATLAB LMI toolbox. Numerical example is given to illustrate 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 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. Arik, S.: An analysis of exponential stability of delayed neural networks with time varying delays. Neural Netw. 17, 1027–1031 (2004)

    Article  MATH  Google Scholar 

  2. Mathiyalagan, K., Sakthivel, R., Anthoni, S.M.: New stability and stabilization criteria for fuzzy neural networks with various activation functions. Phys. Scr. 84, 015007 (2011)

    Article  MATH  Google Scholar 

  3. Fang, Q., Tong, C.B., Yan, J.: A delay decomposition approach for stability of neural networks with time-varing delay. Chinese Phys. B 18, 5203 (2009)

    Article  Google Scholar 

  4. Song, Q., Cao, J.: Impulsive effects on stability of fuzzy Cohen-Grossberg neural networks with time varying delays. IEEE Trans. Syst. Man Cybern. 37, 733–741 (2007)

    Article  Google Scholar 

  5. Ali, M.S., Balasubramaniam, P.: Stability analysis of uncertain fuzzy Hopfield neural networks with time delays. Commun. Nonlinear Sci. Numer. Simulat. 14, 2776–2783 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Li, S., Goa, M., Yang, H.: Delay dependent robust stability for uncertain stochastic fuzzy Hopfield neural networks with time varying delays. Fuzzy Sets Syst. 160, 3503–3517 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Balasubramaniam, P., Chandran, R.: Delay decomposition approach to stability analysis for uncertain fuzzy Hopfield neural networks with time varying delay. Commun. Nonlinear Sci. Numer. Simulat. 16, 2098–2108 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Mahmoud, M.S., Xia, Y.: Improved exponential stability analysis for delayed recurrent neural networks. J. Franklin Inst. 348, 201–211 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Tian, J., Zhou, X.: Improved asymptotic stability criteria for neural networks with interval time varying delay. Expert Syst. Appl. 37, 7521–7525 (2010)

    Article  Google Scholar 

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

    Article  Google Scholar 

  11. 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 

  12. Chen, J., Sun, J., Liu, G.P., Rees, D.: New delay-dependent stability criteria for neural networks with time-varying interval delay. Physics Lett. A 374, 4397–4405 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  13. Souza, F.O., Palhares, R.M.: Interval time-varying delay stability for neural networks. Neurocomputing 73, 2789–2792 (2010)

    Article  Google Scholar 

  14. Takagi, T., Sugeno, M.: Fuzzy identification of system and its applications to modelling and control. IEEE. Trans. Syst. Man Cybern. 15, 116–132 (1985)

    Article  MATH  Google Scholar 

  15. Takagi, T., Sugeno, M.: Stability analysis and design of fuzzy control system. Fuzzy Sets Syst. 45, 135–156 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  16. Zhang, X.M., Han, Q.-L.: A delay decomposition approach to delay dependent stability for linear systems with time varying delays. Int. J. Robust Nonlinear Control 19, 1922–1930 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  17. Xie, L.: Output feedback H ∞  control of systems with parameter uncertainty. Int. J. of Control 63, 741–750 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  18. Han, Q.-L.: A new delay dependent stability creterion for linear neutral systems with norm-bounded uncertainities in all system matrices. Int. J. Syst. Sci. 36, 469–475 (2005)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Government Arts College, Melur, 625 106, Madurai(Dt), Tamilnadu, India

    R. Chandran

  2. Department of Mathematics, Gandhigram Rural Institute - Deemed University, Gandhigram, 624 302, Tamilnadu, India

    R. Chandran & P. Balasubramaniam

Authors
  1. R. Chandran
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Balasubramaniam
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, Gandhigram Rural University, 624302, Gandhigram, Tamil Nadu, India

    P. Balasubramaniam

  2. Department of Mathematics, Gandhigram Rural Institute - Deemed University, 624302, Gandhigram, Tamil Nadu, India

    R. Uthayakumar

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chandran, R., Balasubramaniam, P. (2012). Asymptotic Stability Criterion for Fuzzy Recurrent Neural Networks with Interval Time-Varying Delay. In: Balasubramaniam, P., Uthayakumar, R. (eds) Mathematical Modelling and Scientific Computation. ICMMSC 2012. Communications in Computer and Information Science, vol 283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28926-2_29

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-28926-2_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28925-5

  • Online ISBN: 978-3-642-28926-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation