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H State Estimation of Static Delayed Neural Networks with Non-fragile Sampled-data Control

비결함 샘플 데이타 제어를 가지는 정적 지연 뉴럴 네트웍의 강인 상태추정

  • Liu, Yajuan (Dept. of Electrical Engineering, Yeungnam University) ;
  • Lee, Sangmoon (Dept. of Electronic Engineering, Kyungpook National University)
  • Received : 2016.11.25
  • Accepted : 2016.12.15
  • Published : 2017.01.01

Abstract

This paper studies the state estimation problem for static neural networks with time-varying delay. Unlike other studies, the controller scheme, which involves time-varying sampling and uncertainties, is first employed to design the state estimator for delayed static neural networks. Based on Lyapunov functional approach and linear matrix inequality technique, the non-fragile sampled-data estimator is designed such that the resulting estimation error system is globally asymptotically stable with $H_{\infty}$ performance. Finally, the effectiveness of the developed results is demonstrated by a numerical example.

Keywords

References

  1. I. Varga, G. Elek, H. Zak, On the brain-state-in-a convex-domain neural models, Neural Netw., vol. 9, no. 7, pp. 1173-1184, 1996. https://doi.org/10.1016/0893-6080(96)00028-7
  2. Y. Xia, An extended projection neural network for constrained optimization, Neural Comput., vol. 16, no. 4, pp. 863-883, 2004. https://doi.org/10.1162/089976604322860730
  3. C.-D. Zheng, H. Zhang, and Z. Wang, Delay-dependent globally exponential stability criteria for static neural networks: An LMI approach, IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 56, no. 7, pp. 605-609, 2009. https://doi.org/10.1109/TCSII.2009.2023278
  4. B. Du, J. Lam, Stability analysis of static recurrent neural networks using delay-partitioning and projection, Neural Netw., vol. 22, no. 4, pp. 343-347, 2009. https://doi.org/10.1016/j.neunet.2009.03.005
  5. Z.-G. Wu, J. Lam, H. Su, and J. Chu, Stability and dissipativity analysis of static neural networks with time delay, IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 2, pp. 199-210, 2012. https://doi.org/10.1109/TNNLS.2011.2178563
  6. O.M. Kwon, M.J. Park, Ju H. Park, S.M. Lee, E.J. Cha, New and improved results on stability of static neural networks with interval time-varying delays, Appl. Math. Comput., vol. 239, pp. 346-357, 2014.
  7. Q. Duan, H. Su, Z.-G. Wu, $H_{\infty}$ state estimation of static neural networks with time-varying delay, Neuro-computing, vol. 97, pp. 16-21, 2012.
  8. Y. Liu, S.M. Lee, O.M. Kwon, Ju H. Park, A study on $H_{\infty}$ state estimation of static neural networks with time-varying delays, Appl. Math. Comput., vol. 226, pp. 589-597, 2014.
  9. H. Huang, T. Huang, X. Chen, Guaranteed $H_{\infty}$ performance state estimation of delayed static neural networks, IEEE Trans. Circuits Syst. Express Briefs, vol. 60, no. 6, pp. 371-375, 2013. https://doi.org/10.1109/TCSII.2013.2258258
  10. H. Huang, T. Huang, X. Chen, Further results on guaranteed $H_{\infty}$ performance state estimation of delayed static neural networks, IEEE Trans. Neural Netw. Learn. Syst., vol. 20, no. 6, pp. 1335-1341, 2015.
  11. M.S. Ali, R. Saravanakumar, S. Arik, Novel $H_{\infty}$ state estimation of static neural networks with interval time-varying delays via augmented Lyapunov-Krasovskii functional, Neurocomputing, vol. 171, pp. 949-954, 2016. https://doi.org/10.1016/j.neucom.2015.07.038
  12. T. H. Lee, Ju H. Park, O.M. Kwon, S. M. Lee, Stochastic sample data control for state estimation of time-varying delayed neural networks, Neural Netw., vol. 46, pp. 99-108, 2013. https://doi.org/10.1016/j.neunet.2013.05.001
  13. X.-H. Chang, G.-H. Yang, Nonfragile $H_{\infty}$ filter design for T-F fuzzy systems in standard form, IEEE Trans. Ind. Electron., vol. 61, no. 7, pp. 3448-3458, 2014. https://doi.org/10.1109/TIE.2013.2278955
  14. Y.-Q. Wu, H. Su, R. Lu, Z.-G. Wu, Z. Shu, Passivity -based non-fragile control for Markovian-jump systems with aperiodic sampling, Systems and control, Letters, vol. 84, pp. 35-43, 2015. https://doi.org/10.1016/j.sysconle.2015.08.001
  15. D. Zhang, W. Cai, L. Xie, Q. -G, Wang, Non-fragile distributed filtering for T-F fuzzy systems in sensor networks, IEEE Trans. Fuzzy Syst., vol. 23, no. 5, pp. 1883-1890, 2015. https://doi.org/10.1109/TFUZZ.2014.2367101
  16. K. Gu, V.L. Kharitonov, J. Chen, Stability of Time Delay Systems, Birkhauser, Boston, 2003.
  17. P. Park, J. W. Ko, C. Jeong, Reciprocally convex approach to stability of systems with time-varying delays, Automatica, vol. 47, no. 1, pp. 235-238, 2011. https://doi.org/10.1016/j.automatica.2010.10.014
  18. A. Seuret, F. Gouaisbaut, Wirtinger-based integral inequality : application to time-delay systems, Automatica, vol. 49, no. 8, pp. 2860-2866, 2013. https://doi.org/10.1016/j.automatica.2013.05.030