The Transactions of The Korean Institute of Electrical Engineers (전기학회논문지)

The Korean Institute of Electrical Engineers (대한전기학회)
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Delay-dependent Robust Passivity for Uncertain Neural Networks with Time-varying Delays

시변 지연을 가진 불확실 뉴럴 네트워크에 대한 지연의존 강인 수동성

  • Received : 2011.07.14
  • Accepted : 2011.10.25
  • Published : 2011.11.01
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Abstract

In this paper, the problem of passivity analysis for neural networks with time-varying delays and norm-bounded parameter uncertainties is considered. By constructing a new augmented Lyapunov functional, a new delay-dependent passivity criterion for the network is established in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Two numerical example are included to show the effectiveness of proposed criterion.

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References

  1. J. Cao, "Global asymptotic stability of neural networks with transmission delays", International Journal of System Science, vol.31 pp.1313-1316, 2000. https://doi.org/10.1080/00207720050165807
  2. T. Ensari, S. Arik, "Global stability of a class of neural networks with time-varying delay", IEEE Transactions on Circuits and Systems II-Express Briefs, vol.52, pp.126-130, 2005 https://doi.org/10.1109/TCSII.2004.842050
  3. T. Li, L. Guo, C. Sun, C. Lin, "Further results on delay-dependent stability criteria of neural networks with time-varying delay", IEEE Transactions on Neural Networks, vol.19, pp.726-730, 2008 https://doi.org/10.1109/TNN.2007.914162
  4. O.M. Kwon, J.H. Park, S.M. Lee, "On robust stability for uncertain cellular neural networks with interval time-varying delays", IET Control Theory and Applications, vol.2, pp.625-634, 2008 https://doi.org/10.1049/iet-cta:20070325
  5. Y. Zhang, D. Yue, E. Tian, "New stability criteria of neural networks with interval time-varying delays: A piecewise delay method", Applied Mathematics and Computations, vol.208, pp.249-259, 2009 https://doi.org/10.1016/j.amc.2008.11.046
  6. J.H. Park, "Further results on passivity analysis of delayed cellular neural networks", Chaos Solitons and Fractals, vol.34, pp.1546-1551, 2007 https://doi.org/10.1016/j.chaos.2005.04.124
  7. J.C. Willems, "Dissipative dynamical systems", Archieve for Rational Mechanics and Analysis, vol.45, pp.321-393, 2008
  8. S. Xu, W.X. Zheng, Y. Zou, "Passivity analysis of neural networks with time-varying delays", IEEE Transactions on Circuits and Systems II-Express Briefs, vol.56, pp.325-329, 2009 https://doi.org/10.1109/TCSII.2009.2015399
  9. Y. Chen, W. Li, W. Bi, "Improved results on passivity analysis of uncertain neural networks with time-varying discrete and distributed delays", Neural Processing Letters, vol.30, pp.155-169, 2009 https://doi.org/10.1007/s11063-009-9116-2
  10. J. Fu, H. Zhang, T. Ma, Q. Zhang, "On passivity analysis for stochastic neural networks with interval time-varying delay", Neurocomputing, vol.73, pp. 795-801, 2010 https://doi.org/10.1016/j.neucom.2009.10.010
  11. H.B. Zeng, Y. He, M. Wu, S.P. Xiao, "Passivity analysis for neural networks with a time-varying delay", Neurocomputing, vol.74, pp.730-734, 2011 https://doi.org/10.1016/j.neucom.2010.09.020
  12. Y. Ariba, F. Gouaisbaut, "Delay-dependent stability analysis of linear systems with time-varying delay", Proceedings of 46th IEEE Conference on Decision and Control, December, New Orleans, LA, pp. 2053-2058, 20078
  13. J. Sun, G.P. Liu, J. Chen, "Delay-dependent stability and stabilization of neutral time-delay systems", International Journal of Robust and Nonlinear Control, vol.19, pp.1364-1375, 2009 https://doi.org/10.1002/rnc.1384
  14. R.E. Skelton, T. Iwasaki, K.M. Grigoradis, A unified algebraic approach to linear control design, Taylor and Francisw, New York, 1997
  15. K. Gu, An integral inequality in the stability problem of time-delay systems, Proceedings of39th IEEE Conference on Decision and Control, pp. 2805-2810, 2000.
  16. H. Shao, "New delay-dependent stability criteria for systems with interval delay", Automatica, vol.45, pp.744-749, 2009 https://doi.org/10.1016/j.automatica.2008.09.010
  17. S. Boyd, L.EI Ghaoui, E. Feron, and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia, 1994.