Skip to main content
SpringerLink
Log in

New Stability Criteria for Neural Networks with Distributed and Probabilistic Delays

  • Published:
Circuits, Systems & Signal Processing Aims and scope Submit manuscript

Abstract

This paper is concerned with the stability analysis of neural networks with distributed and probabilistic delays. The probabilistic delay satisfies a certain probability distribution. By introducing a stochastic variable with a Bernoulli distribution, the neural network with random time delays is transformed into one with deterministic delays and stochastic parameters. New conditions for the exponential stability of such neural networks are obtained by employing new Lyapunov–Krasovskii functionals and novel techniques for achieving delay dependence. The proposed conditions reduce the conservatism by considering not only the range of the time delays, but also the probability distribution of their variation. A numerical example is provided to show the advantages of the proposed techniques.

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

Similar content being viewed by others

References

  1. S. Arik, An analysis of exponential stability of delayed neural networks with time varying delays. IEEE Trans. Neural Netw. 17, 1027–1031 (2004)

    MATH  Google Scholar 

  2. S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory (SIAM, Philadelphia, 1994)

    Google Scholar 

  3. J. Cao, J. Wang, Global asymptotic stability of recurrent neural networks with Lipschitz-continuous activation functions and time-varying delays. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 50(1), 34–44 (2003)

    Article  MathSciNet  Google Scholar 

  4. C. Chang, N. Cheng, X. Long, New results on stability analysis of neural networks with time-varying delays. Phys. Lett. A 352, 335–340 (2006)

    Article  Google Scholar 

  5. Y. Chen, W. Su, New robust stability of cellular neural networks with time-varying discrete and distributed delays. Int. J. Innov. Comput. Inf. Control 3(6), 1549–1556 (2007)

    MathSciNet  Google Scholar 

  6. M. Coates, R. Nowark, Sequential Monte Carlo inference of internal delays in nonstationary data networks. IEEE Trans. Signal Process. 50(2), 366–376 (2002)

    Article  Google Scholar 

  7. P. Gahinet, A. Nemirovskii, A.J. Laub, M. Chilali, LMI Control Toolbox User’s Guide (The MathWorks Inc., Natick, 1995)

    Google Scholar 

  8. H. Gao, P. Shi, J. Wang, Parameter-dependent robust stability of uncertain time-delay systems. J. Comput. Appl. Math. 206(1), 366–373 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  9. H. Gao, C. Wang, Delay-dependent robust H ∞ and L 2-L ∞ filtering for a class of uncertain nonlinear time-delayed systems. IEEE Trans. Automat. Contr. 48(9), 1661–1666 (2003)

    Article  MathSciNet  Google Scholar 

  10. K. Gu, V. Kharitonov, J. Chen, Stability of Time-Delay Systems (Springer, Berlin, 2003)

    MATH  Google Scholar 

  11. Y. He, J. She, M. Wu, Delay-dependent exponential stability of delayed neural networks with time-varying delay. IEEE Trans. Circuits Syst. II Express Briefs 53(7), 553–557 (2006)

    Article  Google Scholar 

  12. E. Knightly, H-bind: a new approach to providing statistical performance guarantees to VBR traffic, in Proceedings of IEEE INFOCOM, San Francisco, CA, March 1996

  13. T. Liao, J. Yan, C. Cheng, C. Hwang, Globally exponential stability condition of a class of neural networks with time-varying delays. Phys. Lett. A 339, 333–342 (2005)

    Article  MATH  Google Scholar 

  14. X. Liao, K. Wong, J. Yu, Novel stability conditions for cellular neural networks with time delay. Int. J. Bifurc. Chaos Appl. Sci. Eng. 11, 1853–1864 (2001)

    Article  Google Scholar 

  15. F. Presti, N. Duffield, J. Horowitz, D. Towsley, Multicast-based inference of network-internal delay distributions. IEEE ACM Trans. Netw. 10(6), 761–775 (2002)

    Article  Google Scholar 

  16. A. Robinson, An application of recurrent neural nets to phone probability estimation. IEEE Trans. Neural Netw. 5(2), 298–305 (1994)

    Article  Google Scholar 

  17. P. Shi, Filtering on sampled-data systems with parametric uncertainty. IEEE Trans. Automat. Contr. 43(7), 1022–1027 (1998)

    Article  MATH  Google Scholar 

  18. P. Shi, K. Boukas, R.K. Agarwal, Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delays. IEEE Trans. Automat. Contr. 44(11), 2139–2144 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  19. P. Shi, J. Zhang, J. Qiu, L. Xing, New global asymptotic stability criterion for neural networks with discrete and distributed delays. Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng. 221(I1), 129–135 (2007)

    Article  Google Scholar 

  20. Y. Tsang, M. Coates, R. Nowark, Network delay tomography. IEEE Trans. Signal Process. 51(8), 2125–2136 (2003)

    Article  Google Scholar 

  21. R. Wang, J. Zhao, Exponential stability analysis for discrete-time switched linear systems with time-delay. Int. J. Innov. Comput. Inf. Control 3(6), 1557–1564 (2007)

    Google Scholar 

  22. S. Wang, R. Nathuji, R. Battati, W. Zhao, Providing statistical delay guarantees in wireless networks, in Proceedings of the 24th International Conference on Distributed Computing Systems (ICDCS’04) (2004)

  23. Y. Wang, L. Xie, C.E.D. Souza, Robust control of a class of uncertain nonlinear system. Syst. Control. Lett. 19, 139–149 (1992)

    Article  Google Scholar 

  24. Z. Wang, Y. Liu, K. Fraser, X. Liu, Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays. Phys. Lett. A 354, 288–297 (2006)

    Article  Google Scholar 

  25. Z. Wang, Y. Liu, X. Liu, On global asymptotic stability of neural networks with discrete and distributed delays. Phys. Lett. A 345(4–6), 299–308 (2005)

    Article  MATH  Google Scholar 

  26. S. Xu, J. Lam, A new approach to exponential stability analysis of neural networks with time-varying delays. Neural Netw. 19(1), 76–83 (2006)

    Article  MATH  Google Scholar 

  27. S. Xu, J. Lam, D. Ho, Y. Zou, Novel global asymptotic stability criteria for delayed cellular neural networks. IEEE Trans. Circuits Syst. II Express Briefs 52(6), 33–36 (2005)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, 150001, China

    Rongni Yang & Huijun Gao

  2. Department of Mechanical Engineering, University of Hong Kong, Hong Kong, China

    James Lam

  3. Faculty of Advanced Technology, University of Glamorgan, Pontypridd, CF37 1DL, UK

    Peng Shi

  4. Institute for Logistics and Supply Chain Management, School of Computer Science and Mathematics, Victoria University, Melbourne, Australia

    Peng Shi

  5. School of Mathematics and Statistics, University of South Australia, Adelaide, South Australia, Australia

    Peng Shi

Authors
  1. Rongni Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huijun Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. James Lam
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Peng Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rongni Yang.

Additional information

This work was partially supported by National Natural Science Foundation of China (60528007 and 60825303), the Research Fund for the Doctoral Programme of Higher Education of China (20070213084), RGC HKU 7028/04P, Hong Kong, China, and EPSRC (EP/F029195), UK.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yang, R., Gao, H., Lam, J. et al. New Stability Criteria for Neural Networks with Distributed and Probabilistic Delays. Circuits Syst Signal Process 28, 505–522 (2009). https://doi.org/10.1007/s00034-008-9092-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-008-9092-1

Keywords

Search

Navigation