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

The Korean Institute of Electrical Engineers (대한전기학회)
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Robust ℋ∞ Sampled-Data Control for Takagi-Sugeno Fuzzy Model with Singular Perturbation

특이섭동 타카기-수게노 퍼지모델의 강인 ℋ∞ 샘플치 제어

  • Received : 2016.04.28
  • Accepted : 2016.08.18
  • Published : 2016.09.01
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Abstract

This paper deals with a robust $H_{\infty}$ sampled-data controller design problem for nonlinear systems in Takagi-Sugeno fuzzy form with singular perturbation. The employed controller takes a state-feedback form. The design condition is represented in terms of linear matrix inequalities. A numerical examples is included to show the effectiveness of the theoretical development.

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References

  1. W. D. McComb, "The physics of fluid turbulence," Chem. Phys., vol. 1, 1990.
  2. W. Assawinchaichote and S. K. Nguang, "$H_{\infty}$ fuzzy control design for nonlinear singularly perturbed systems with pole placement constraints: an LMI approach," IEEE Trans. Syst., Man, Cybern. B, vol. 34, pp. 579-588, 2004. https://doi.org/10.1109/TSMCB.2003.817087
  3. W. Assawinchaichote, S. K. Nguang, and P. Shi, "$H_{\infty}$ output feedback control design for uncertain fuzzy singularly perturbed systems: an LMI approach," Automatica, vol. 40, pp. 2147-2152, 2004.
  4. M. Suzuki and M. Miura, "Stabilizing feedback controllers for singularly perturbed linear constant systems,"IEEE Trans. Autom. Control, vol. 21, pp. 123-124, 1976. https://doi.org/10.1109/TAC.1976.1101151
  5. J. O'Reilly, "Full-order observers for a class of singularly perturbed linear time-varying systems," Int. J. Control, vol. 30, pp. 745-756, 1979. https://doi.org/10.1080/00207177908922811
  6. Z. H. Shao and M. E. Sawan, "Robust stability of singularly perturbed systems," Int. J. Control, vol. 58, pp. 1469-1476, 1993. https://doi.org/10.1080/00207179308923065
  7. T. Grodt and Z. Gajic, "The recursive reduced-order numerical solution of the singularly perturbed matrix differential Riccati equation," IEEE Trans. Autom. Control, vol. 33, pp. 751-754, 1988. https://doi.org/10.1109/9.1291
  8. W. Assawinchaichote and S. K. Nguang, "Fuzzy observerbased controller design for singularly perturbed nonlinear systems: An LMI approach," Proc. of the 41th IEEE Conf. on Decision and Control, vol. 2, pp. 2165-2170, 2002.
  9. T. H. S. Li and K. J. Lin, "Composite fuzzy control of nonlinear singularly perturbed systems," IEEE Trans. Fuzzy Syst., vol. 15, pp. 176-187, 2007. https://doi.org/10.1109/TFUZZ.2006.878252
  10. M. H. Asemani and V. J. Majd, "A robust $H_{\infty}$ non-pdc design scheme for singularly perturbed T-S fuzzy systems with immeasurable state variables," IEEE Trans. Fuzzy Syst., vol. 23, pp. 525-541, 2015. https://doi.org/10.1109/TFUZZ.2014.2317253
  11. E. Fridman, "Near-optimal $H_{\infty}$ control of linear singularly perturbed systems," IEEE Trans. Autom. Control, vol. 41, no. 2, pp. 236-240, 1996. https://doi.org/10.1109/9.481525
  12. W. Tan, T. Leung, and Q. Tu, "$H_{\infty}$ control for singularly perturbed systems," Automatica, vol. 34, no. 2, pp. 255-260, 1998. https://doi.org/10.1016/S0005-1098(97)00183-0
  13. H. Liu, F. Sun, and Y. Hu, "$H_{\infty}$ control for fuzzy singularly perturbed systems," Fuzzy Sets Syst., vol. 155, no. 2, pp. 272-291, 2005. https://doi.org/10.1016/j.fss.2005.05.004
  14. D. W. Kim and H. J. Lee, "Direct discrete-time design approach to robust $H_{\infty}$ sampled-data observer-based output-feedback fuzzy control," Int. J. Syst. Sci., vol. 47, pp. 1-15, 2015.
  15. H. J. Lee and D. W. Kim, "Performance -recoverable intelligent digital redesign for fuzzy tracking controllers," Inform. Sci., vol. 326, pp. 350-367, 2016. https://doi.org/10.1016/j.ins.2015.08.003
  16. S. C. Jee and H. J. Lee, "Sampled-data H_/$H_{\infty}$ Hfault detection and isolation for nonlinear systems in T-S form: An approximate model approach," Fuzzy Sets Syst., 2016.
  17. S. C. Jee, H. J. Lee, and D. W. Kim, "Detecting sensor fault for nonlinear systems in T-S form under sampled-data measurement: exact direct discrete-time design approach," Int. J. Control Autom. Syst., vol. 14, no. 2, pp. 1-9, 2016. https://doi.org/10.1007/s12555-015-2000-0
  18. E. Fridman, "Robust sampled-data control of linear singularly perturbed systems," in Proceedings of the 44th IEEE conference on decision and control, 2005, pp. 4324-4329.
  19. E. Fridman, "Robust $H{\infty}$ sampled-data control of linear singularly perturbed systems," IEEE Trans. Autom. Control, vol. 51, no. 3, pp. 470-475, 2006. https://doi.org/10.1109/TAC.2005.864194
  20. J. H. Moon, J. J. Lee and H. J. Lee, "Sampled-Data Controller Design for Nonlinear Systems Including Singular Perturbation in Takagi-Sugeno Form," Journal of Korean Institute of Intelligent Systems, vol. 26, pp. 050-055, 2016. https://doi.org/10.5391/JKIIS.2016.26.1.050
  21. K. Gu, "An integral inequality in the stability problem of time-delay systems," in Proc. of the 39th IEEE Conf. on Decision and Control, 2000, pp. 2805-2810.
  22. B.-S. Chen, C.-S. Tseng, and H.-J. Uang, "Robustness design of nonlinear dynamic systems via fuzzy linear control," IEEE Trans. FuzzySyst., vol. 7, no.5, pp. 571-585, 1999.
  23. K. Tanaka, T. Ikeda, and H. O. Wang, "Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs," IEEE Trans. Fuzzy Syst., vol. 6, pp. 250-265, 1998 https://doi.org/10.1109/91.669023
  24. D. W. Kim and H. J. Lee, "Comments on "T-S fuzzy model-based robust $H_{\infty}$ design for networked control systems with uncertainties," IEEE Trans. Ind. Informat., vol. 5, no. 4, p. 507, 2009. https://doi.org/10.1109/TII.2009.2017525
  25. H. K. Lam, H. Li, C. Deters, E. L. Secco, H. A. Wurdemann, and K. Althoefer, "Control design for interval type-2 fuzzy systems under imperfect premise matching," IEEE Trans. Ind. Electron., vol. 61, pp. 956-968, 2014. https://doi.org/10.1109/TIE.2013.2253064
  26. W.-J. Chang, C.-P. Kuo, and C.-C. Ku, "Intelligent fuzzy control with imperfect premise matching concept for complex nonlinear multiplicative noised systems," Neurocomputing, vol. 154, pp. 276-283, 2015. https://doi.org/10.1016/j.neucom.2014.11.065
  27. D. Zhang and Q.-L. Han, "$H{\infty}$ control design for network-based T-S fuzzy systems with asynchronous constraints on membership functions," IECON 2011-37th Annual Conference on IEEE Industrial Electronics Society, pp. 2584-2589, 2011.
  28. H. K. Lam and W. K. Ling, "Sampled-data fuzzy controller for continuous nonlinear systems," IET Contrl Theory Appl., vol. 2, no. 1, pp. 32-39, 2008. https://doi.org/10.1049/iet-cta:20070126
  29. H. Liu, F. Sun, and Z. Sun, "Stability analysis and synthesis of fuzzy singularly perturbed systems," IEEE Trans. Fuzzy Syst., vol. 13, no. 2, pp. 273-284, Apr 2005. https://doi.org/10.1109/TFUZZ.2004.839660