Delay-dependent Stability Criteria for Uncertain Stochastic Neural Networks with Interval Time-varying Delays

구간 시변 지연이 존재하는 불확실 확률적 뉴럴 네트웍의 지연의존 안전성 판별법

  • Published : 2008.11.01

Abstract

In this paper, the problem of global asymptotic stability of uncertain stochastic neural networks with delay is considered. The delay is assumed to be time-varying and belong to a given interval. Based on the Lyapunov stability theory, new delay-dependent stability criteria for the system is derived in terms of LMI(linear matrix inequality). Three numerical examples are given to show the effectiveness of proposed method.

Keywords

References

  1. M. Ramesh, S. Narayanan, Chaos control of Bonhoeffer-van der Pol oscillator using neural networks, Chaos Soliton Fract., Vol.12, pp. 2395-2405, 2001 https://doi.org/10.1016/S0960-0779(00)00200-9
  2. M. Cannas, S. Cincotti, M. Marchesi, F. Pilo, Learning of Chua's circut attactors by locally recurrent neural networks, Chaos Soliton Fract., Vol.12, pp.2109-2115, 2001 https://doi.org/10.1016/S0960-0779(00)00174-0
  3. K. Oawara, L.T. Fan, A. Tsutsumi, T. Yano, K. Kuramoto, K. Yoshida, An articial neural network as a model for chaotic behavior of a therr-phase fluidized bed, Chaos Soliton Fract., Vol. 13, pp.353-362, 2002 https://doi.org/10.1016/S0960-0779(00)00250-2
  4. J. Cao, Global asymptotic stability of neural networks with transmission delays, Int. J. Syst. Sci., Vol.31 , pp.1313-1316, 2000 https://doi.org/10.1080/00207720050165807
  5. S. Arik, An analysis of global asymptotic stability of delayed cellular neural networks, IEEE T. Neural Network, Vol.13, pp.1239-1242, 2002 https://doi.org/10.1109/TNN.2002.1031957
  6. S. Arik, An improved global stability result for delayed cellular neural networks, IEEE T. Circuits-I, Vol.49, pp.1211-1214, 2002 https://doi.org/10.1109/TCSI.2002.801264
  7. S. Ruan, R.S. Filfil, Dynamics of a two-neuron system with discrete and distributed delays, Physica D, Vol.191 , pp.323-342, 2004 https://doi.org/10.1016/j.physd.2003.12.004
  8. J.H. Pak, A new stability analysis of delayed cellular neural networks, Appl. Math. Comput., Vol.181, pp.200-205, 2006 https://doi.org/10.1016/j.amc.2006.01.024
  9. J.H. Park, A delay-dependent asymptotic stability criterion of cellular neural networks with time-varying discrete and distributed delays, Chaos Soliton Fract., Vol.33, pp.436-442. 2007 https://doi.org/10.1016/j.chaos.2006.01.015
  10. J.H. Park, An analysis of global robust stability of uncertain cellular nerual networks with discrete and distributed delays, Chaos Soliton Fract., Vol.32, pp.800-807, 2007 https://doi.org/10.1016/j.chaos.2005.11.106
  11. S. Xu, J. Lam, D.W.C. HO, A new LMI conditions for delay-dependent asymptotic satbility of delayed hopfield neural networks, IEEE T Circuit-II., Vol.53, pp.230-234, 2006 https://doi.org/10.1109/TCSII.2005.857764
  12. S. Xu, J. Lam, A new approach to exponential stability analysis of neural networks with time-var${\gamma}$ing delays, Neural Network., 19, 76-83(2006) https://doi.org/10.1016/j.neunet.2005.05.005
  13. A. Chen, J. Cao, L. Huang, An Estimation of upper bound of delays for global asymptotical stability of delayed Hopfield neual networks, IEEE Trans. Circuits and Syst. I, Vol.49, pp.1028-1032, 2002 https://doi.org/10.1109/TCSI.2002.800841
  14. Q. Zang, X. Wei, J. Xu, Delay-dependent exponential stability of cellular neural networks with time-varying delays, Chaos Soliton Fract., Vol.23, pp.1363-1369, 2005 https://doi.org/10.1016/S0960-0779(04)00391-1
  15. H. Yang, T. Chu, C. Zhang, Exponential stability of neural networks with variable delays via LMI approach, Chaos Soliton Fract., Vol.30, pp.133-139, 2006 https://doi.org/10.1016/j.chaos.2005.08.134
  16. L. Rong, LMI-based criteria for robust stability of Cohen-Grossberg neural networks with delay, Physics Lett. A, Vol.339, pp.63-73, 2005 https://doi.org/10.1016/j.physleta.2005.03.023
  17. W. Wang, J. Cao, LMI-based criteria for globally robust stability of delayed Cohen-Grossberg neural networks, IEE Proc.-Control Theory Appl., Vol.53, pp.397-402, 2006
  18. N. Qzcan, S. Arik, Global robust stability analysis of neural networks with multiple time delays, IEEE T. Circuit-I, Vol.53, pp.166-176, 2006 https://doi.org/10.1109/TCSI.2005.855724
  19. J. Cao, J. Wang, Global robust asymptotic and robust stability of recurrent neural networks with time delays, IEEE Trans. Circuits Syst.-Fundam.Theory Appl., Vol.52, pp.417-426, 2005 https://doi.org/10.1109/TCSI.2004.841574
  20. H. Liu, G. Chen, Delay-dependent stability for neural networks with time-varying delay, Chaos Soliton Fract., Vol.33, pp.171-177, 2007 https://doi.org/10.1016/j.chaos.2006.01.025
  21. S. Haykin, Neural Networks - A Comprehensive Foundation, Prentice-Hal, NJ, 1998
  22. J. Zhang, P. Shi, J Qiu, Novel robust stability criteria for uncertain stochastic Hopfield neural networks with time-varying delays, Nonlinear Anal Real, Vol8, pp.1349-1357, 2007 https://doi.org/10.1016/j.nonrwa.2006.06.010
  23. H. Huang, G. Feng, Delay-dependent stability for uncertain stochastic nerual networks with time-varying delay, Phsyica A, Vol.381, pp.93-103, 2007 https://doi.org/10.1016/j.physa.2007.04.020
  24. H. Huang, G. Feng, Corrigendum to 'Delay-dependent stability for uncertain stochastic neural networks with time-varying delay'. Physica A doi:10.1016/j.physa2007.10.016(2007)
  25. V.L Karitonov, S.-I. Niculescu, On the stability of linear systems with uncertain delay, IEEE T. Automat Contr. Vol.48, pp.127-132, 2003 https://doi.org/10.1109/TAC.2002.806665
  26. D. Yue, C. Pang, G.Y. Tang, Guaranteed cost control of linear systems over networks with state and input quantisations, IEE P.-Contr. Ap. Vol.153, pp.658-664, 2006 https://doi.org/10.1049/ip-cta:20050294
  27. W. Michies, V.V. Assche, S.-I. Niculescu, Stabilization of time-delay systems with a controlled time varying delay and applications, IEEE T. Automat Contr. Vol.50, pp.493-504, 2005 https://doi.org/10.1109/TAC.2005.844723
  28. K.W. Yu, C.H. Lien, Stability criteria for uncertain neural systems with interval time-varying delays, Chaos Soliton Fract. doi:10.1016/j.chaos.2007.01.002, 2007
  29. S. Boyd, L. El. Ghanoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Philadelphia, SIAM, 1994
  30. K. Gu, An integral inequality in the stability problem of time-delay systems, Proceedings of 39th IEEE Conference on Decision and Control, Sydney, Australia, December, 2000
  31. L. Arnold, Stochastic Differential Equations Theory and Applications, Wiley, New York, 1972
  32. X. Mao, Stochastic Differential Equations and Their Applications, Chichester, Horwood, UK, 1997
  33. R.Z. Khasminskii, Stochastic Stability of Differential Equations. Alphen aan den Rjin, Sjithoffand Noor, Khasminskiidhoff, 1980
  34. P. Gahinet, A. Nemirovskii, A. Laub, M. Chliali, LMI Toolbox, The Mathworks, Massachusetts, 1995