Skip to main content
SpringerLink
Log in

Robust stability analysis of delayed Takagi-Sugeno fuzzy Hopfield neural networks with discontinuous activation functions

  • Research article
  • Published:
Cognitive Neurodynamics Aims and scope Submit manuscript

Abstract

In this paper, the global robust stability problem of delayed Takagi–Sugeno fuzzy Hopfield neural networks with discontinuous activation functions (TSFHNNs) is considered. Based on Lyapunov stability theory and M-matrices theory, we derive a stability criterion to guarantee the global robust stability of TSFHNNs. Compared with the existing literature, we remove the assumptions on the neuron activations such as Lipschitz conditions, bounded, monotonic increasing property or the assumption that the right-limit value is bigger than the left one at the discontinuous point. Finally, two numerical examples are given to show the effectiveness of the proposed stability results.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Forti M, Nistri P (2003) Global convergence of neural networks with discontinuous neuron activations. IEEE Trans Circuits Syst I Fundam Theory Appl 50(11):1421–1435

    Article  Google Scholar 

  2. Forti M, Nistri P (2005) Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain. IEEE Trans Neural Netw 16(6):1449–1463

    Article  PubMed  Google Scholar 

  3. Forti M, Grazzini M, Nistri P, Pancioni L (2006) Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations. IEEE Trans Neural Netw 214(6):88–99

    Google Scholar 

  4. Wang J, Huang L, Guo Z (2009) Dynamical behavior of delayed Hopfield neural networks with discontinuous activations. Appl Math Model 33(1):1793–1802

    Article  Google Scholar 

  5. Li L, Huang L (2009) Dynamical behaviors of a class of recurrent neural networks with discontinuous neuron activations. Appl Math Model. doi:http://www.dx.doi.org/10.1016/j.apm.2009.03.014

  6. Lu W, Chen T (2005) Dynamical behaviors of Cohen-Grossberg neural networks with discontinuous activation functions. Neural Netw 18(1):231–242

    Article  Google Scholar 

  7. Meng Y et al (2009) Stability analysis of Cohen-Grossberg neural networks with discontinuous neuron activations. Appl Math Model. doi:http://www.dx.doi.org/10.1016/j.apm.2009.04.016

  8. Lu W, Chen T (2006) Dynamical behaviors of delayed neural network systems with discontinuous activation functions. Neural Comput 18(1):683–708

    Article  Google Scholar 

  9. Wang Y, et al. (2008) Global robust stability of delayed neural networks with discontinuous activation functions. IET Control Theory Appl 7(2):543–553

    Article  Google Scholar 

  10. Zuo Y et al (2009) Robust stability criterion for delayed neural networks with discontinuous activation functions. Neural Process Lett 29(1):29–44

    Article  CAS  Google Scholar 

  11. Papini D, Taddei V (2005) Global exponential stability of the periodic solution of a delayed neural network with discontinuous activations. Phys Lett A 343(2):117–128

    Article  CAS  Google Scholar 

  12. Huang L, Wang J, Zhou X (2009) Existence and global asymptotic stability of periodic solutions for Hopfield neural networks with discontinuous activations. Nonlinear Anal Real World Appl 10(3):1651–1661

    Article  Google Scholar 

  13. Wu H, Shan C (2009) Stability analysis for periodic solution of BAM neural networks with discontinuous neuron activations and impulses. Appl Math Model 33(6):2564–2574

    Article  Google Scholar 

  14. Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst Man Cybern 15(1):116–132

    Google Scholar 

  15. Hou Y, Liao T, Yan J (2007) Stability analysis of Takagi-Sugeno fuzzy cellular neural networks with time-varying delays. IEEE Trans Syst Man Cybern 37(3):720–726

    Article  Google Scholar 

  16. Huang H, Ho DWC, Lam J (2005) Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays. IEEE Trans Circuits Syst I Reg Pap 52(5):251–255

    Article  Google Scholar 

  17. Cao Y, Frank RM (2000) Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach. IEEE Trans Fuzzy Syst 8(2):200–211

    Article  Google Scholar 

  18. Liu Y, Tang W (2004) Exponential stability of fuzzy cellular neural networks with constant and time-varying delays. Phys Lett A 323(3):224–233

    Article  CAS  Google Scholar 

  19. Syed Ali M, Balasubramaniam P (2009) Stability analysis of uncertain fuzzy Hopfield neural networks with time delays. Commun Nonlinear Sci Numer Simulat 14(1):2776–2783

    Article  Google Scholar 

  20. Lou X, Cui B (2007) Robust asymptotic stability of uncertain fuzzy BAM neural networks with time-varying delays. Fuzzy Set Syst 158(24):2746–2756

    Article  Google Scholar 

  21. Wai R, Yang Z (2008) Adaptive fuzzy neural network control design via a T-S fuzzy model for a robot manipulator including actuator dynamics. IEEE Trans Syst Man Cybern 38(5):1326–1346

    Article  Google Scholar 

  22. Filippov A (1988) Differential equations with discontinuous right-hand side. Kluwer, Boston

    Google Scholar 

  23. Aubin J, Cellina A (1984) Differential inclusions. Springer, Berlin

    Google Scholar 

Download references

Acknowledgments

This work was supported by National Natural Science Foundation of China (10771055, 60775047, 60835004), and National High Technology Research and Development Program of China (863 Program: 2007AA04Z244, 2008AA04Z214), Graduate Innovation Foundation of Hunan Province (2010).

Author information

Authors and Affiliations

  1. College of Electric and Information Technology, Hunan University, 410082, Changsha, Hunan, People’s Republic of China

    Xiru Wu & Yaonan Wang

  2. College of Mathematics and Econometrics, Hunan University, 410082, Changsha, Hunan, People’s Republic of China

    Lihong Huang

  3. School of Energy and Power Engineering, Changsha University of Science and Technology, 410004, Changsha, Hunan, People’s Republic of China

    Yi Zuo

Authors
  1. Xiru Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yaonan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lihong Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yi Zuo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Xiru Wu or Yaonan Wang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, X., Wang, Y., Huang, L. et al. Robust stability analysis of delayed Takagi-Sugeno fuzzy Hopfield neural networks with discontinuous activation functions. Cogn Neurodyn 4, 347–354 (2010). https://doi.org/10.1007/s11571-010-9123-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11571-010-9123-z

Keyword

Search

Navigation