Static Output Feedback Control for Continuous T-S Fuzzy Systems

연속시간 T-S 퍼지 시스템에 대한 정적 출력궤환 제어

  • Jeung, Eun Tae (Department of Control and Instrumentation Engineering, Changwon National University)
  • 정은태 (창원대학교 제어계측공학과)
  • Received : 2014.03.07
  • Accepted : 2014.03.13
  • Published : 2015.06.01


This paper presents a design method of a static output feedback controller for continuous T-S fuzzy systems via parallel distributed compensation (PDC). The existence condition of a set of static output feedback gains is represented in terms of linear matrix inequalities (LMIs). The sufficient condition presented here does not need any transformation matrices and equality constraints and is less conservative than the previous results seen in [20].


Supported by : 창원대학교


  1. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modeling and control," IEEE Trans. Systems, Man, Cybernetics, vol. 15, no. 1, pp. 116-132, 1985.
  2. H. Wang, K. Tanaka, and M. Griffin, "Parallel distributed compensation of nonlinear systems by Takagi and Sugeno's fuzzy model," in Proc. FUZZ-IEEE, Yokohama, Japan, pp. 531-538, 1995.
  3. H. O. Wang, K. Tanaka, and M. F. Griffin, "An approach to fuzzy control of nonlinear systems: Stability and design issues," IEEE Trans. Fuzzy Systems, vol. 4, no. 1, pp. 14-23, Feb. 1996.
  4. E. Kim and H. Lee, "New approaches to relaxed quadratic stability condition of fuzzy control systems," IEEE Trans. Fuzzy Systems, vol. 8, no. 5, pp. 523-534, Oct. 2000.
  5. X. Liu and Q. Zang, "Approaches to Quadratic Stability Conditions and $H{\infty}$ Control Designs for T-S Fuzzy Systems," IEEE Trans. Fuzzy Systems, vol. 11, no. 6, pp. 830-839, Dec. 2003.
  6. D. Lee, H. C. Sung, and Y. H. Joo, "Fuzzy modeling and robust stability analysis of wind farm based on prediction model for wind speed," J. Institute of Control, Robotics and Systems(in Korean), vol. 20, no. 1, pp. 22-28, 2014.
  7. X.-J. Ma and Z.-Q. Sun, "Analysis and design of fuzzy reduced-dimensional observer and fuzzy functional observer," Fuzzy Sets and Systems, vol. 120, pp. 35-63, 2001.
  8. K. R. Lee, J. H. Kim, E. T. Jeung, and H. B. Park, "Output feedback robust $H{\infty}$ control of uncertain fuzzy dynamic systems with time-varying delay," IEEE Trans. Fuzzy Systems, vol. 8, no. 6, pp. 657-664, Dec. 2000.
  9. V. L. Syrmos, C. T. Abdallah, P. Dorato, and K. Grigoriadis, "Static output feedback - a survey," Automatica, vol. 33, no. 2, pp. 125-137, 1997.
  10. L. E. Ghaoui, F. Oustry, and M. AitRami, "A cone complementarity linearization algorithm for static output-feedback and related problems," IEEE Trans. Automatic Control, vol. 42, no. 8, Aug. 1997.
  11. M. Nachidi, A. Benzaouia, F. Tadeo, and M. A. Rami, "LMI-based approach for output-feedback stabilization for discrete-time Takagi-Sugeno systems," IEEE Trans. Fuzzy Systems, vol. 16, no. 5, pp. 1188-1196, Oct. 2008.
  12. M. Nachidi, F. Tadeo, A. Benzaouia, and M. A. Rami, "Static output-feedback for Tagaki-Sugeno systems with delays," Int. J. Adaptive Control & Signal Processing, vol. 25, pp. 295-312, 2011.
  13. J.-C. Lo and M.-L. Lin, "Robust $H{\infty}$ nonlinear control via fuzzy static output feedback," IEEE Trans. Circuits and Systems-1: Fundamental Theory and Applications, vol. 50, no. 11, pp. 1494-1502, 2003.
  14. W. Chang, J. B. Park, Y. H. Joo, and G. Chen, "Static output-feedback fuzzy controller for Chen's chaotic system with uncertainties," Information Sciences, vol. 151, pp. 227-244, 2003.
  15. C.-H. Fang, Y.-S. Liu, S.-W. Kau, L. Hong, and C.-H. Lee, "A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems," IEEE Trans. Fuzzy Systems, vol. 14, no. 3, pp. 386-397, Jun. 2006.
  16. S. C. Jee, J. H. Moon, and H. J. Lee, "Static output-feedback-based robust fault tolerant controller design," J. Institute of Control, Robotics and Systems(in Korean), vol. 19, no. 7, pp. 587-591, 2013.
  17. S.-W. Kau, H. J. Lee, C.-M. Yang, C.-H. Lee, L. Hong, and C.-H. Fang, "Robust $H{\infty}$ fuzzy static output feedback control of T-S fuzzy systems with parametric uncertainties," Fuzzy Sets and Systems, vol. 158, pp. 135-146, 2007.
  18. H. J. Lee and D. W. Kim, "Robust stabilization of T-S fuzzy systems: Fuzzy static output feedback under parametric uncertainty," Int. J. Control, Automation, and Systems, vol. 7, no. 5, pp. 731-736, 2009.
  19. G. B. Koo, J. B. Park, and Y. H. Joo, "Robust fuzzy controller for Large-scale nonlinear systems using decentralized static output feedback," Int. J. Control, Automation, and Systems, vol. 9, no. 4, pp. 649-658, 2011.
  20. E. T. Jeung and K. R. Lee, "Static output feedback control for continuous-time T-S fuzzy systems: An LMI approach," Int. J. Control, Automation, and Systems, vol. 12, no. 3, pp. 703-708, 2014.