Skip to main content
SpringerLink
Log in

Passivity analysis for discrete-time switched neural networks with various activation functions and mixed time delays

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

Abstract

This paper is concerned with the passivity analysis for a class of discrete-time switched neural networks with various activation functions and mixed time delays. The mixed time delays under consideration include time-varying discrete delay and bounded distributed delay. By using the average dwell time approach and the discontinuous piecewise Lyapunov function technique, a novel delay-dependent sufficient condition for exponential stability of the switched neural networks with passivity is derived in terms of a set of linear matrix inequalities (LMIs). The obtained condition is not only dependent on the discrete delay bound, but also dependent on the distributed delay bound. A numerical example is given to demonstrate the effectiveness of the proposed result.

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

    Google Scholar 

  2. Haykin, S.: Neural Networks: A Comprehensive Foundation. Prentice Hall, New York (1998)

    Google Scholar 

  3. Wang, Z., Liu, Y., Liu, X.: 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 

  4. 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 

  5. Li, H., Chen, B., Zhou, Q., Fang, S.: Robust exponential stability for uncertain stochastic neural networks with discrete and distributed time-varying delays. Phys. Lett. A 372(19), 3385–3394 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Wu, Z., Su, H., Chu, J., Zhou, W.: New results on robust exponential stability for discrete recurrent neural networks with time-varying delays. Neurocomputing 72, 3337–3342 (2009)

    Article  Google Scholar 

  7. Li, H., Chen, B., Zhou, Q., Qian, W.: Robust stability for uncertain delayed fuzzy Hopfield neural networks with Markovian jumping parameters. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 39(1), 94–102 (2009)

    Article  Google Scholar 

  8. Wu, Z., Su, H., Chu, J., Zhou, W.: Improved delay-dependent stability condition of discrete recurrent neural networks with time-varying delays. IEEE Trans. Neural Netw. 21(4), 692–697 (2010)

    Article  Google Scholar 

  9. Zeng, Z., Huang, T., Zheng, W.: Multistability of recurrent neural networks with time-varying delays and the piecewise linear activation function. IEEE Trans. Neural Netw. 21(8), 1371–1378 (2010)

    Article  Google Scholar 

  10. Zhao, J., Hill, D.J., Liu, T.: Synchronization of complex dynamical networks with switching topology: a switched system point of view. Automatica 45(11), 2502–2511 (2009)

    Article  MATH  Google Scholar 

  11. Yuan, K., Cao, J., Li, H.: Robust stability of switched Cohen–Grossberg neural networks with mixed time-varying delays. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 36(6), 1356–1363 (2006)

    Article  Google Scholar 

  12. Li, P., Cao, J.: Global stability in switched recurrent neural networks with time-varying delay via nonlinear measure. Nonlinear Dyn. 49(1–2), 295–305 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. Ahn, C.K.: An H∞ approach to stability analysis of switched Hopfield neural networks with time-delay. Nonlinear Dyn. 60(4), 703–711 (2010)

    Article  MATH  Google Scholar 

  14. Liberzon, D.: Switching in Systems and Control. Birkhauser, Basel (2003)

    Book  MATH  Google Scholar 

  15. Qiu, J., Feng, G., Yang, J.: New results on robust energy-to-peak filtering for discrete-time switched polytopic linear systems with time-varying delay. IET Control Theory Appl. 2(9), 795–806 (2008)

    Article  MathSciNet  Google Scholar 

  16. Wu, L., Feng, Z., Zheng, W.: Exponential stability analysis for delayed neural networks with switching parameters: Average dwell time approach. IEEE Trans. Neural Netw. 21(9), 1396–1407 (2010)

    Article  Google Scholar 

  17. Lian, J., Zhang, K.: Exponential stability for switched Cohen–Grossberg neural networks with average dwell time. Nonlinear Dyn. 63(3), 331–343 (2011)

    Article  MathSciNet  Google Scholar 

  18. 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 

  19. Park, J.H.: Further results on passivity analysis of delayed cellular neural networks. Chaos Solitons Fractals 34(5), 1546–1551 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  20. Song, Q., Liang, J., Wang, Z.: Passivity analysis of discrete-time stochastic neural networks with time-varying delays. Neurocomputing 72(7–9), 1782–1788 (2009)

    Article  Google Scholar 

  21. Lu, C., Liao, C., Tsai, H.: Delay-range-dependent global robust passivity analysis of discrete-time uncertain recurrent neural networks with interval time-varying delay. Discrete Dyn. Nat. Soc. 2009, 14 (2009). Article ID 430158

    MathSciNet  Google Scholar 

  22. Chen, Y., Wang, H., Xue, A., Lu, R.: Passivity analysis of stochastic time-delay neural networks. Nonlinear Dyn. 61(1–2), 71–82 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  23. Li, H., Wang, C., Shi, P., Gao, H.: New passivity results for uncertain discrete-time stochastic neural networks with mixed time delays. Neurocomputing 73(16–18), 3291–3299 (2010)

    Article  Google Scholar 

  24. Liu, Y., Wang, Z., Liu, X.: Asymptotic stability for neural networks with mixed time delays: the discrete-time case. Neural Netw. 22, 67–74 (2009)

    Article  Google Scholar 

  25. Liu, Y., Wang, Z., Liang, J., Liu, X.: Synchronization and state estimation for discrete-time complex networks with distributed delays. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 38(5), 1314–1325 (2008)

    Article  MathSciNet  Google Scholar 

  26. Liu, Y., Wang, Z., Liang, J., Liu, X.: Stability and synchronization of discrete-time Markovian jumping neural networks with mixed mode-dependent time delays. IEEE Trans. Neural Netw. 20(7), 1102–1116 (2009)

    Article  Google Scholar 

  27. Jiang, X., Han, Q., Yu, X.: Stability criteria for linear discrete-time systems with interval-like time-varying delay. In: Proceeding of the American Control Conference, Portland, OR, USA, June 8–10, 2005

    Google Scholar 

  28. He, Y., Liu, G.P., Rees, D., Wu, M.: H ∞ filtering for discrete-time systems with time-varying delay. Signal Process. 89, 275–282 (2009)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Automation, Zhejiang Provincial United Key Laboratory of Embedded Systems, Zhejiang University of Technology, Hangzhou, 310032, P.R. China

    Dan Zhang & Li Yu

Authors
  1. Dan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Li Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dan Zhang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, D., Yu, L. Passivity analysis for discrete-time switched neural networks with various activation functions and mixed time delays. Nonlinear Dyn 67, 403–411 (2012). https://doi.org/10.1007/s11071-011-9988-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-011-9988-3

Keywords

Search

Navigation