DOI QR코드

DOI QR Code

시변 지연이 존재하는 불확실 퍼지 뉴럴 네트워크의 강인 안정성 판별법에 대한 새로운 리아프노프 함수법

A New Augmented Lyapunov Functional Approach to Robust Stability Criteria for Uncertain Fuzzy Neural Networks with Time-varying Delays

  • 권오민 (충북대학교 전기공학부) ;
  • 박명진 (충북대학교 전기공학부) ;
  • 이상문 (대구대학교 전자공학부) ;
  • 박주현 (영남대학교 전기공학과)
  • 투고 : 2011.08.03
  • 심사 : 2011.09.29
  • 발행 : 2011.11.01

초록

This paper proposes new delay-dependent robust stability criteria for neural networks with time-varying delays. By construction of a suitable Lyapunov-Krasovskii's (L-K) functional and use of Finsler's lemma, new stability criteria for the networks are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed methods.

키워드

참고문헌

  1. L. O. Chua, and L. Yang, "Cellular neural networks: Applications", IEEE Trans. Circuits Syst. vol. 35, no. 1, pp. 1273-1290, 1988. https://doi.org/10.1109/31.7601
  2. A. Cichocki, and R. Unbehauen, Neural Networks for Optimization and Signal Processing, Hoboken, NJ: Wiely, 1993.
  3. G. Joya, M.A> Atencia, and F. Sandoval, "Hopfield neural networks for optimization: Study of the different dynamics", Neurocomputing, vol.43, no.1-4, pp. 219-237, 2002. https://doi.org/10.1016/S0925-2312(01)00337-X
  4. W.J. Li, and T. Lee, "Hopfield neural networks for affine invariant matching", IEEE Trans. Neural Netw. vol. 12, no. 6, pp. 1400-1410, 2001. https://doi.org/10.1109/72.963776
  5. S. Arik, "An analysis of global asymptotic stability of delayed cellular neural networks", IEEE Trans. Neural Networks, vol.13, pp.1239-1242, 2002. https://doi.org/10.1109/TNN.2002.1031957
  6. 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
  7. Ju H. Park, "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
  8. O.M. Kwon, Ju H. Park, S.M. Lee, "Delay-dependent stability criteria for uncertain stochastic neural networks with interval time-varying daleys", Trans. KIEE, vol.57, pp.2066-2073, 2008.
  9. J. P. Richard, "Time-delay systems: an overview of some recent advances and open problems", Automatica, vol.39, pp.1667-1694, 2003. https://doi.org/10.1016/S0005-1098(03)00167-5
  10. K. Gu, "An integral inequality in the stability problem of time-delay systems", in: The 39th IEEE Conf. Decision Control, Sydney, Australia, Dec. 2000, pp.2805-2810.
  11. S. Xu, J. Lam, "On equivalent and efficiency of certain stability criteria for time-delay systems", IEEE Trans. Autom. Control, vol.52, pp.95-101, 2007. https://doi.org/10.1109/TAC.2006.886495
  12. T. Takagi, M. Sugeno, "Fuzzy identification of systems and its application to modeling and control", IEEE Trans. Syst. Man. Cybern., vol.15, pp.116-132, 1985.
  13. C.H. Lien, K.W. Yu, W.D. Chen, Z.L. Wan, Y.J. Chung, "Stability criteria for uncertain Takagi-Sugeno fuzzy systems with interval time-varying delay", IET Proc. Control Theory Appl., vol.1, pp. 764-769, 2007. https://doi.org/10.1049/iet-cta:20060299
  14. Z. Yang, Y.P. Yang, "New delay-dependnet stability anaylsis and synthesis of T-S fuzzy systems with time-varing delay", Int. J. Robust Nonlinear Control, vol.20, pp.313-322, 2010. https://doi.org/10.1002/rnc.1431
  15. Q. Zhang, R. Xiang, "Global asymptotic stability of fuzzy cellular neural networks with time-varying delays", Phys. Lett. A, vol.372, pp.3971-3977, 2008. https://doi.org/10.1016/j.physleta.2008.01.063
  16. P. Balasubramaniam, R. Chandran, "Delay decomposition approach to stability analysis for uncertain fuzzy Hopfield neural networks with time-varying delay", Commun. Nonlinear Sci. Numer. Simulat., vol. 16, pp.2098-2108, 2011. https://doi.org/10.1016/j.cnsns.2010.08.019
  17. S. Boyd, L.EI Ghaoui and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia, 1994.
  18. P. G. Park, "A delay-dependent stability criteria for systems with uncertain time-invariant delays", IEEE Trans. Autom. Control, vol.44, pp.876-877, 1999. https://doi.org/10.1109/9.754838
  19. M.C. de Oliveira, R.E. Skelton. Stability tests for constrained linear systems. Springer, Berlin, 2001.
  20. H. Shao, New delay-dependent stability criteria for systems with interval delay, Automatica, vol.45, No.3, pp. 744-749, 2009. https://doi.org/10.1016/j.automatica.2008.09.010
  21. K. Gu, "A further refinement of discretized Lyapunov functional method for stability of time-delay systems", International Journal of Control, vol.74, no.10, pp. 967-976, 2001. https://doi.org/10.1080/00207170110047190
  22. T. Li, L. Guo, and L. Wu, "Simplified approach to the asymptotical stability of linear systems with interval time-varying delay", vol.3, no.2, pp. 252-260, 2008.
  23. C. Peng, and Y.C. Tian, "Delay-dependent robust stability criteria for uncertain systems with interval time-varying delay", Journal of Computational and Applied Mathematics, vol. 214, no. 2, pp. 480-494, 2008 https://doi.org/10.1016/j.cam.2007.03.009
  24. E. Fridman, U. Shaked, and K. Liu, "New conditions for delay-derivative-dependent stability", Automatica, vol.45, no.11, 2009.
  25. O. M. Kwon, "Stability criteria for uncertain stochastic dynamic systems with time-varying delays", International Journal of Robust and Nonlinear Control, vol.21, pp.338-350, 2011. https://doi.org/10.1002/rnc.1600