DOI QR코드

DOI QR Code

T-S 퍼지 시스템에 대한 비병렬분산보상 정적 출력궤환 제어

Non-PDC Static Output Feedback Control for T-S Fuzzy Systems

  • 정은태 (창원대학교 제어계측공학과)
  • Jeung, Eun Tae (Control and Instrumentation Engineering, Changwon National University)
  • 투고 : 2016.03.03
  • 심사 : 2016.05.17
  • 발행 : 2016.07.01

초록

This paper presents a design method of non-parallel distributed compensation (non-PDC) static output feedback controller for continuous- and discrete-time T-S fuzzy systems. The existence condition of static output feedback control law is represented in terms of linear matrix inequalities (LMIs). The proposed sufficient stabilizing condition does not need any transformation matrices and equality constraints and is less conservative than the previous result of [21].

키워드

과제정보

연구 과제 주관 기관 : 창원대학교

참고문헌

  1. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modeling and control," IEEE Transactions on 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," Proceedings of 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 Transactions on Fuzzy Systems, vol. 4, no. 1, pp. 14-23, Feb. 1996. https://doi.org/10.1109/91.481841
  4. E. Kim and H. Lee, "New approaches to relaxed quadratic stability condition of fuzzy control systems," IEEE Transactions on Fuzzy Systems, vol. 8, no. 5, pp. 523-534, Oct. 2000. https://doi.org/10.1109/91.873576
  5. X. Liu and Q. Zang, "Approaches to Quadratic Stability Conditions and $H_{{\infty}}$ Control Designs for T-S Fuzzy Systems," IEEE Transactions on Fuzzy Systems, vol. 11, no. 6, pp. 830-839, Dec. 2003. https://doi.org/10.1109/TFUZZ.2003.819834
  6. 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. https://doi.org/10.1016/S0165-0114(99)00145-1
  7. 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 Transactions on Fuzzy Systems, vol. 8, no. 6, pp. 657-664, Dec. 2000. https://doi.org/10.1109/91.890325
  8. L. E. Ghaoui, F. Oustry, and M. AitRami, "A cone complementarity linearization algorithm for static output-feedback and related problems," IEEE Transactions on Automatic Control, vol. 42, no. 8, Aug. 1997.
  9. Y. Y. Cao, J. Lam, and Y. X. Sun, "Static output feedback stabilization: An ILMI approach," Automatica, vol. 34, no. 12, pp. 1641-1645, 1998. https://doi.org/10.1016/S0005-1098(98)80021-6
  10. D. Huang and S. K. Nguang, "Robust $H_{{\infty}}$ static output feedback control of fuzzy systems: An ILMI approach," IEEE Transactions on Systems, Man, Cybernetics-Part B: Cybernetics, vol. 36, no. 1, pp. 216-222, 2006. https://doi.org/10.1109/TSMCB.2005.856145
  11. D. Huang and S. K. Nguang, "Static output feedback controller design for fuzzy systems: An ILMI approach," Information Sciences, vol. 177, pp. 3005-3015, 2007. https://doi.org/10.1016/j.ins.2007.02.014
  12. M. Nachidi, A. Benzaouia, F. Tadeo, and M. A. Rami, "LMI-based approach for output-feedback stabilization for discrete-time Takagi-Sugeno systems," IEEE Transactions on Fuzzy Systems, vol. 16, no. 5, pp. 1188-1196, Oct. 2008. https://doi.org/10.1109/TFUZZ.2008.924338
  13. M. Nachidi, F. Tadeo, A. Benzaouia, and M. A. Rami, "Static output-feedback for Tagaki-Sugeno systems with delays," International Journal of Adaptive Control & Signal Processing, vol. 25, pp. 295-312, 2011. https://doi.org/10.1002/acs.1196
  14. J.-C. Lo and M.-L. Lin, "Robust $H_{{\infty}}$ nonlinear control via fuzzy static output feedback," IEEE Transactions on Circuits and Systems-1: Fundamental Theory and Applications, vol. 50, no. 11, pp. 1494-1502, 2003. https://doi.org/10.1109/TCSI.2003.818623
  15. 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. https://doi.org/10.1016/S0020-0255(02)00297-9
  16. 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 Transactions on Fuzzy Systems, vol. 14, no. 3, pp. 386-397, Jun. 2006. https://doi.org/10.1109/TFUZZ.2006.876331
  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. https://doi.org/10.1016/j.fss.2006.09.010
  18. H. J. Lee and D. W. Kim, "Robust stabilization of T-S fuzzy systems: Fuzzy static output feedback under parametric uncertainty," International Journal of Control, Automation, and Systems, vol. 7, no. 5, pp. 731-736, 2009. https://doi.org/10.1007/s12555-009-0505-0
  19. G. B. Koo, J. B. Park, and Y. H. Joo, "Robust fuzzy controller for Large-scale nonlinear systems using decentralized static output feedback," International Journal of Control, Automation, and Systems, vol. 9, no. 4, pp. 649-658, 2011. https://doi.org/10.1007/s12555-011-0405-y
  20. E. T. Jeung and K. R. Lee, "Static output feedback control for continuous-time T-S fuzzy systems: An LMI approach," International Journal of Control, Automation, and Systems, vol. 12, no. 3, pp. 703-708, 2014. https://doi.org/10.1007/s12555-013-0427-8
  21. E. T. Jeung, "Static output feedback control for continuous T-S fuzzy systems," Journal of Institute of Control, Robotics and Systems (in Korean), vol. 21, no. 6, pp. 560-564, 2015. https://doi.org/10.5302/J.ICROS.2015.15.0041
  22. T. M. Guerra and L. Vermeiren, "LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form," Automatica, vol. 40, pp. 823-829, 2004. https://doi.org/10.1016/j.automatica.2003.12.014
  23. B. Ding, "Stabilization of Takagi-Sugeno model via nonparallel distributed compensation law," IEEE Transactions on Fuzzy Systems, vol. 18, no. 1, pp. 188-194, Feb. 2010. https://doi.org/10.1109/TFUZZ.2009.2033192
  24. W.-J. Chang, C.-C. Ku, and C.-H. Chang, "PDC and non-PDC fuzzy control with relaxed stability conditions for continuous-time multiplicative noised fuzzy systems," Journal of the Franklin Institute, vol. 349, pp. 2664-2686, 2012. https://doi.org/10.1016/j.jfranklin.2012.06.004
  25. D. W. Kim, "$H_{{\infty}}$ sampled-data control of Kakagi-Sugeno fuzzy system," Journal of Institute of Control, Robotics and Systems, vol. 20, no. 11, pp. 1142-1146, 2014. https://doi.org/10.5302/J.ICROS.2014.14.8021