Advertisement

Nonlinear Dynamics

, Volume 67, Issue 2, pp 1695–1707 | Cite as

Passivity of uncertain neural networks with both leakage delay and time-varying delay

  • Qiankun Song
  • Jinde CaoEmail author
Original Paper

Abstract

In this paper, the passivity problem is investigated for a class of uncertain neural networks with leakage delay and time-varying delay as well as generalized activation functions. By constructing appropriate Lyapunov–Krasovskii functionals, and employing Newton–Leibniz formulation and the free-weighting matrix method, several delay-dependent criteria for checking the passivity of the addressed neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Two examples with simulations are given to show the effectiveness and less conservatism of the proposed criteria.

Keywords

Passivity Neural networks Uncertainty Leakage delay Time-varying delay Linear matrix inequality 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Chen, T.: Global exponential stability of delayed Hopfield neural networks. Neural Netw. 14(8), 977–980 (2001) CrossRefGoogle Scholar
  2. 2.
    Arik, S.: An analysis of exponential stability of delayed neural networks with time varying delays. Neural Netw. 17(7), 1027–1031 (2004) CrossRefzbMATHGoogle Scholar
  3. 3.
    Cao, J., Song, Q.: Stability in Cohen–Grossberg-type bidirectional associative memory neural networks with time-varying delays. Nonlinearity 19(7), 1601–1617 (2006) CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Liu, Y., Wang, Z., Liu, X.: Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Netw. 19(5), 667–675 (2006) CrossRefzbMATHGoogle Scholar
  5. 5.
    Wang, Z., Liu, Y., Liu, X.: State estimation for jumping recurrent neural networks with discrete and distributed delays. Neural Netw. 22(1), 41–48 (2009) CrossRefGoogle Scholar
  6. 6.
    Akhmet, M., Aruğaslan, D., Yilmaz, E.: Stability analysis of recurrent neural networks with piecewise constant argument of generalized type. Neural Netw. 23(7), 805–811 (2010) CrossRefGoogle Scholar
  7. 7.
    Souza, F., Palhares, R.: Interval time-varying delay stability for neural networks. Neurocomputing 73(13–15), 789–2792 (2010) Google Scholar
  8. 8.
    Ozcan, N., Arik, S.: A new sufficient condition for global robust stability of bidirectional associative memory neural networks with multiple time delays. Nonlinear Anal., Real World Appl. 10(5), 3312–3320 (2009) CrossRefMathSciNetGoogle Scholar
  9. 9.
    Park, J.: Further note on global exponential stability of uncertain cellular neural networks with variable delays. Appl. Math. Comput. 188(1), 850–854 (2007) CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Singh, V.: New LMI-based criteria for global robust stability of delayed neural networks. Appl. Math. Model. 34(10), 2958–2965 (2010) CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Gau, R., Lien, C., Hsieh, J.: Novel stability conditions for interval delayed neural networks with multiple time-varying delays. Int. J. Innov. Comput., Inf. Control 7(1), 433–444 (2011) Google Scholar
  12. 12.
    Niculescu, S., Lozano, R.: On the passivity of linear delay systems. IEEE Trans. Autom. Control 46(3), 460–464 (2001) CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Fridman, E., Shaked, U.: On delay-dependent passivity. IEEE Trans. Autom. Control 47(4), 664–669 (2002) CrossRefMathSciNetGoogle Scholar
  14. 14.
    Gao, H., Chen, T., Chai, T.: Passivity and passification for networked control systems. SIAM J. Control Optim. 46(4), 1299–1322 (2007) CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Liang, J., Wang, Z., Liu, X.: Robust passivity and passification of stochastic fuzzy time-delay systems. Inf. Sci. 180(9), 1725–1737 (2010) CrossRefzbMATHGoogle Scholar
  16. 16.
    Liang, J., Wang, Z., Liu, X.: On passivity and passification of stochastic fuzzy systems with delays: The discrete-time case. IEEE Trans. Syst. Man Cybern. 40(3), 964–969 (2010) CrossRefMathSciNetGoogle Scholar
  17. 17.
    Li, C., Liao, X.: Passivity analysis of neural networks with time delay. IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process. 52(8), 471–475 (2005) CrossRefMathSciNetGoogle Scholar
  18. 18.
    Park, J.: Further results on passivity analysis of delayed cellular neural networks. Chaos Solitons Fractals 34(5), 1546–1551 (2007) CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Lou, X., Cui, B.: Passivity analysis of integro-differential neural networks with time-varying delays. Neurocomputing 70(4–6), 1071–1078 (2007) Google Scholar
  20. 20.
    Lu, C., Tsai, H., Su, T., Tsai, J., Liao, C.: A delay-dependent approach to passivity analysis for uncertain neural networks with time-varying delayed. Neural Process. Lett. 27(3), 237–246 (2008) CrossRefGoogle Scholar
  21. 21.
    Li, H., Gao, H., Shi, P.: New passivity analysis for neural networks with discrete and distributed delays. IEEE Trans. Neural Netw. 21(11), 1842–1847 (2010) CrossRefGoogle Scholar
  22. 22.
    Zhang, Z., Mou, S., Lam, J., Gao, H.: New passivity criteria for neural networks with time-varying delay. Neural Netw. 22(7), 864–868 (2009) CrossRefGoogle Scholar
  23. 23.
    Chen, Y., Li, W., Bi, W.: Improved results on passivity analysis of uncertain neural networks with time-varying discrete and distributed delays. Neural Process. Lett. 30(2), 155–169 (2009) CrossRefGoogle Scholar
  24. 24.
    Xu, S., Zheng, W., Zou, Y.: Passivity analysis of neural networks with time-varying delays. IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process. 56(4), 325–329 (2009) CrossRefGoogle Scholar
  25. 25.
    Chen, B., Li, H., Lin, C., Zhou, Q.: Passivity analysis for uncertain neural networks with discrete and distributed time-varying delays. Phys. Lett. A 373(14), 1242–1248 (2009) CrossRefMathSciNetGoogle Scholar
  26. 26.
    Zhu, S., Shen, Y., Chen, G.: Exponential passivity of neural networks with time-varying delay and uncertainty. Phys. Lett. A 375(2), 136–142 (2010) CrossRefMathSciNetGoogle Scholar
  27. 27.
    Balasubramaniam, P., Nagamani, G., Rakkiyappan, R.: Global passivity analysis of interval neural networks with discrete and distributed delays of neutral type. Neural Process. Lett. 32(2), 109–130 (2010) CrossRefGoogle Scholar
  28. 28.
    Chen, Y., Wang, H., Xue, A., Lu, R.: Passivity analysis of stochastic time-delay neural networks. Nonlinear Dyn. 61(1–2), 71–82 (2010) CrossRefzbMATHMathSciNetGoogle Scholar
  29. 29.
    Zeng, H., He, Y., Wu, M., Xiao, S.: Passivity analysis for neural networks with a time-varying delay. Neurocomputing 74(5), 730–734 (2011) CrossRefGoogle Scholar
  30. 30.
    Fu, J., Ma, T., Zhang, Q.: On passivity analysis for stochastic neural networks with interval time-varying delay. Neurocomputing 73(4–6), 795–801 (2010) CrossRefGoogle Scholar
  31. 31.
    Song, Q., Wang, Z.: New results on passivity analysis of uncertain neural networks with time-varying delays. Int. J. Comput. Math. 87(3), 668–678 (2010) CrossRefzbMATHMathSciNetGoogle Scholar
  32. 32.
    Gopalsamy, K.: Leakage delays in BAM. J. Math. Anal. Appl. 325(2), 1117–1132 (2007) CrossRefzbMATHMathSciNetGoogle Scholar
  33. 33.
    Li, C., Huang, T.: On the stability of nonlinear systems with leakage delay. J. Franklin Inst. 346(4), 366–377 (2009) CrossRefzbMATHMathSciNetGoogle Scholar
  34. 34.
    Peng, S.: Global attractive periodic solutions of BAM neural networks with continuously distributed delays in the leakage terms. Nonlinear Anal., Real World Appl. 11(3), 2141–2151 (2010) CrossRefzbMATHMathSciNetGoogle Scholar
  35. 35.
    Li, X., Fu, X., Balasubramaniam, P., Rakkiyappan, R.: Existence, uniqueness and stability analysis of recurrent neural networks with time delay in the leakage term under impulsive perturbations. Nonlinear Anal., Real World Appl. 11(5), 4092–4108 (2010) CrossRefzbMATHMathSciNetGoogle Scholar
  36. 36.
    Li, X., Cao, J.: Delay-dependent stability of neural networks of neutral type with time delay in the leakage term. Nonlinearity 23(7), 1709–1726 (2010) CrossRefzbMATHMathSciNetGoogle Scholar
  37. 37.
    Balasubramaniam, P., Nagamani, G., Rakkiyappan, R.: Passivity analysis for neural networks of neutral type with Markovian jumping parameters and time delay in the leakage term. Commun. Nonlinear Sci. Numer. Simul. 16(11), 4422–4437 (2011) CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of MathematicsChongqing Jiaotong UniversityChongqingP.R. China
  2. 2.Department of MathematicsSoutheast UniversityNanjingP.R. China

Personalised recommendations