Skip to main content
SpringerLink
Log in

Passivity analysis of stochastic time-delay neural networks

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Passivity analysis of stochastic neural networks with time-varying delays and parametric uncertainties is investigated in this paper. Passivity of stochastic neural networks is defined. Both delay-independent and delay-dependent stochastic passivity conditions are presented in terms of linear matrix inequalities (LMIs). The results are established by using the Lyapunov–Krasovskii functional method. In order to derive the delay-dependent passivity criterion, some free-weighting matrices are introduced. The effectiveness of the method is illustrated by numerical examples.

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. Haykin, S.: Neural Networks: A Comprehensive Foundation. Prentice-Hall, Englewood Cliffs (1998)

    Google Scholar 

  2. Shams, S.: Neural network optimization for multi-target multi-sensor passive tracking. Proc. IEEE 84(10), 1442–1457 (1996)

    Article  Google Scholar 

  3. Ruiz, A., Owens, D.H., Townley, S.: Existence, learning, and replication of periodic motion in recurrent neural networks. IEEE Trans. Neural Netw. 9(4), 651–661 (1998)

    Article  Google Scholar 

  4. Ren, X.M., Rad, A.B.: Identification of nonlinear systems with unknown time delay based on time-delay neural networks. IEEE Trans. Neural Netw. 18(5), 1536–1541 (2007)

    Article  Google Scholar 

  5. Mi, L., Takeda, F.: Analysis on the robustness of the pressure-based individual identification system based on neural networks. Int. J. Innov. Comput., Inf. Control 3(1), 97–110 (2007)

    Google Scholar 

  6. Fekih, A., Xu, H., Chowdhury, F.: Neural networks based system identification techniques for model-based fault detection of nonlinear systems. Int. J. Innov. Comput., Inf. Control 3(5), 1073–1085 (2007)

    Google Scholar 

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

    MATH  Google Scholar 

  8. Xu, S., Lam, J.: On equivalence and efficiency of certain stability criteria for time-delay systems. IEEE Trans. Automat. Control 52(1), 95–101 (2007)

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

  10. Li, L., Jia, Y., Du, J., Yuan, S.: Robust L 2−L ∞ control for uncertain singular systems with time-varying delay. Prog. Nat. Sci. 18, 1015–1021 (2008)

    Article  MathSciNet  Google Scholar 

  11. Peng, C., Tian, Y.-C.: Improved delay-dependent robust stability criteria for uncertain systems with interval time-varying delay. IET Control Theory Appl. 2(9), 752–761 (2008)

    Article  MathSciNet  Google Scholar 

  12. Michel, A., Liu, D.: Qualitative Analysis and Synthesis of Recurrent Neural Networks. Dekker, New York (2002)

    MATH  Google Scholar 

  13. Baldi, P., Atiya, A.F.: How delays affect neural dynamics and learning. IEEE Trans. Neural Netw. 5(3), 612–621 (1994)

    Article  Google Scholar 

  14. Cao, J.: Periodic solutions and exponential stability in delayed cellular neural networks. Phys. Rev. E 60, 3244–3248 (1999)

    Article  MathSciNet  Google Scholar 

  15. 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 

  16. Singh, V.: Robust stability of cellular neural networks with delay: linear matrix inequality approach. IEE Proc. Control Theory Appl. 151, 125–129 (2004)

    Article  Google Scholar 

  17. 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  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    MathSciNet  Google Scholar 

  20. Xu, J., Pi, D., Cao, Y.-Y., Zhong, S.: On stability of neural networks by a Lyapunov functional-based approach. IEEE Trans. Circuits Syst. I, Regul. Pap. 54(4), 912–924 (2007)

    Article  MathSciNet  Google Scholar 

  21. Lu, C., Su, T., Su, Y., Huang, S.: A delay-dependent approach to stability for static recurrent neural networks with mixed time-varying delays. Int. J. Innov. Comput., Inf. Control 4(7), 1661–1672 (2008)

    Google Scholar 

  22. Wu, H., Sun, J., Zhong, X.: Analysis of dynamical behaviors for delayed neural networks with inverse Lipschitz neuron activations and impulses. Int. J. Innov. Comput., Inf. Control 4(3), 705–716 (2008)

    Google Scholar 

  23. Xia, L., Xia, M., Liu, L.: LMI conditions for global asymptotic stability of neural networks with discrete and distributed delays. ICIC Express Lett. 2(3), 257–262 (2008)

    Google Scholar 

  24. Yi, J., Yang, G., Zhu, Y., Tang, Z.: Dynamics analysis and a coefficient tuning method in a chaotic neural network. ICIC Express Lett. 2(4), 323–330 (2008)

    Google Scholar 

  25. Mou, S., Gao, H., Lam, J., Qiang, W.: A new criterion of delay-dependent asymptotic stability for Hopfield neural networks with time delay. IEEE Trans. Neural Netw. 19(3), 532–535 (2008)

    Article  Google Scholar 

  26. Zhang, H., Wang, Z., Liu, D.: Global asymptotic stability of recurrent neural networks with multiple time-varying delays. IEEE Trans. Neural Netw. 19(5), 855–872 (2008)

    Article  MathSciNet  Google Scholar 

  27. Shao, H.: Delay-dependent approaches to globally exponential stability for recurrent neural networks. IEEE Trans. Circuits Syst. II, Exp. Briefs 55(6), 591–595 (2008)

    Article  Google Scholar 

  28. Blythe, S., Mao, X., Liao, X.: Stability of stochastic delay neural networks. J. Franklin Inst. 338, 481–495 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  29. Longtin, A., Milton, J.G., Bos, H.E., Mackey, C.: Noise and critical behavior of the pupil light reflex at oscillations onset. Phys. Rev. A 41, 6992–7005 (1990)

    Article  Google Scholar 

  30. Cabrera, J.L., Milton, J.G.: On–off intermittency in a human balancing task. Phys. Rev. Lett. 89(15), 158702 (2002)

    Article  Google Scholar 

  31. Stoica, A.-M., Yaesh, I.: Markovian jump delayed Hopfield networks with multiplicative noise. Automatica 44, 2157–2162 (2008)

    Article  MathSciNet  Google Scholar 

  32. Wang, Z., Shu, H., Fang, J., Liu, X.: Robust stability for stochastic Hopfield neural networks with time delays. Nonlinear Anal., Real World Appl. 7, 1119–1128 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  33. Zhang, J., Shi, P., Qiu, J.: Novel robust stability criteria for uncertain stochastic Hopfield neural networks with time-varying delays. Nonlinear Anal., Real World Appl. 8, 1349–1357 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  34. Huang, H., Feng, G.: Delay-dependent stability for uncertain stochastic neural networks with time-varying delay. Physica A 381, 93–103 (2007)

    Article  Google Scholar 

  35. Li, X., Cao, J.: Delay-independent exponential stability of stochastic Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion terms. Nonlinear Dyn. 50, 363–371 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  36. Chen, W.-H., Lu, X.: Mean square exponential stability of uncertain stochastic delayed neural networks. Phys. Lett. A 372, 1061–1069 (2008)

    Article  MathSciNet  Google Scholar 

  37. Chen, Y., Xue, A., Zhao, X., Zhou, S.: Improved delay-dependent stability analysis for uncertain stochastic Hopfield neural networks with time-varying delays. IET Control Theory Appl. 3, 88–97 (2009)

    Article  MathSciNet  Google Scholar 

  38. Lozano, R., Brogliato, B., Egeland, O., Maschke, B.: Dissipative Systems Analysis and Control: Theory and Applications. Springer, London (2000)

    MATH  Google Scholar 

  39. Commuri, S., Lewis, F.L.: CMAC neural networks for control of nonlinear dynamical systems: structure, stability, and passivity. Automatica 33(4), 635–641 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  40. Yu, W., Li, X.: New results on system identification with dynamic neural networks. IEEE Trans. Neural Netw. 12, 412–417 (2001)

    Article  Google Scholar 

  41. Yu, W.: Passivity analysis for dynamic multilayer neuro-identifier. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 50(1), 173–178 (2003)

    Article  Google Scholar 

  42. Li, C., Liao, X.: Passivity analysis of neural networks with time delays. IEEE Trans. Circuits Syst. II, Exp. Briefs 52(8), 471–475 (2005)

    Article  MathSciNet  Google Scholar 

  43. Lou, X., Cui, B.: Passivity analysis of integro-differential neural networks with time-varying delays. Neurocomputing 70, 1071–1078 (2007)

    Article  Google Scholar 

  44. Park, J.H.: Further results on passivity analysis of delayed cellular neural networks. Chaos Solitons Fractals 34, 1546–1551 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  45. Khas’miniskii, R.Z.: Stochastic Stability of Differential Equations. S & N International Publisher, Rockville (1980)

    Google Scholar 

  46. Mao, X.: Stochastic Differential Equations and Applications. Horwood, Chichester (1997)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Operational Research and Cybernetics, Hangzhou Dianzi University, Hangzhou, 310018, P.R. China

    Yun Chen

  2. Institute of Automation, Zhejiang Sci-Tech University, Hangzhou, 310018, P.R. China

    Huijiao Wang

  3. Institute of Information and Control, Hangzhou Dianzi University, Hangzhou, 310018, P.R. China

    Anke Xue & Renquan Lu

Authors
  1. Yun Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huijiao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anke Xue
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Renquan Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Huijiao Wang.

Additional information

This work was supported in part by the National Basic Research Program of China (973 Program) under grant 2009CB320602, the National Natural Science Foundation of China under Grants 60434020, 60974138, the Zhejiang Povincial Natural Science Foundation of China under grant Y1090465.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, Y., Wang, H., Xue, A. et al. Passivity analysis of stochastic time-delay neural networks. Nonlinear Dyn 61, 71–82 (2010). https://doi.org/10.1007/s11071-009-9632-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-009-9632-7

Keywords

Search

Navigation