Analysis and design of an affine fuzzy system via bilinear matrix inequality

IEEE Transactions on Fuzzy Systems

Volumn 13, Issue 1, 2005, Pages 115-123

  Kim, Euntai ^a   Lee, Chang Hoon ^b   Cho, Young Wan ^c  

^a Yonsei University   (South Korea)

^b PaiChai University   (South Korea)

^c Seokyeong University   (South Korea)

Author keywords

Affine fuzzy system; Bilinear matrix inequality (BMI); Diffeomorphism; Linear matrix inequality (LMI); Stability; Stabilizability

Indexed keywords

COMPUTER SIMULATION; CONTROL SYSTEM ANALYSIS; CONTROL SYSTEM SYNTHESIS; MATHEMATICAL MODELS; MATRIX ALGEBRA; SYSTEM STABILITY;

AFFINE FUZZY SYSTEM; BILINEAR MATRIX INEQUALITY (BMI); DIFFEOMORPHISM; LINEAR MATRIX INEQUALITY (LMI); STABILIZABILITY;

FUZZY CONTROL;

EID: 14644443576     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2004.836074     Document Type: Article

References (21)

1. H. Yamamoto and T. Furuhashi, "A new sufficient condition for stable fuzzy control system and its design method," IEEE Trans. Fuzzy Syst. vol. 9, no. 4, pp. 554-569, Apr. 2001.
2. H. Han, C. Y. Su, and S. Murakami, "Adaptive fuzzy control for a class of discrete-time nonlinear systems," in Proc. 10th IEEE Int. Conf. Fuzzy Systems, vol. 2, 2002, pp. 892-895.
3. B.-J. Park, W. Pedrycz, and S.-K. Oh, "Identification of fuzzy models with the aid of evolutionary data granulation," Proc. Inst. Elect. Eng. - Control Theory Appl., vol. 148, no. 5, pp. 406-418, 2001.
4. R. Palm, D. Driankov, and H. Hellendoorn, Model Based Fuzzy Control Berlin, Germany: Springer-Verlag, 1996.
5. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modeling and control," IEEE Trans. Syst. Man Cybern. vol. SMC-15, no. 1, pp. 116-132, Feb. 1985.
6. K. Tanaka and M. Sugeno, "Stability analysis and design of fuzzy control systems," Fuzzy Sets Syst., vol. 45, pp. 136-156, 1992.
7. K. Tanaka and M. Sano, "A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer," IEEE Trans. Fuzzy Syst., vol. 2, no. 2, pp. 119-134, May 1994.
8. B. S. Chen, C.-S. Tseng, and H.-J. Uang, "Robustness design of nonlinear dynamic systems via fuzzy linear control," IEEE Trans. Fuzzy Syst., vol. 7, no. 5, pp. 571-585, Oct. 1999.
9. M. C. M. Teixeira and S. H. Żak, "Stabilizing controller design for uncertain nonlinear systems using fuzzy models," IEEE Trans. Fuzzy Syst., vol. 7, no. 2, pp. 133-142, Apr. 1999.
10. E. Kim and D. Kim, "Stability analysis and synthesis for an affine fuzzy system via LMI and ILMI: Discrete case," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 31, no. 1, pp. 132-140, Feb. 2001.
11. E. Kim and S. Kim, "Stability analysis and synthesis for an affine fuzzy control system via LMI and ILMI: Continuous case," IEEE Trans. Fuzzy Syst., vol. 10, no. 3, pp. 391-400, Jun. 2002.
12. T. A. Johansen, K. J. Hunt, and P. J. Gawthrop, "Transient performance, robustness and off-equilibrium linearization in fuzzy gain scheduled control," in Adv. Fuzzy Control, D. Driankov and R. Palm, Eds., pp. 357-375.
13. J. P. Marin and A. Titli, "Robust quadratic stabilizability of nonhomogeneous Sugeno's systems ensuring completeness of the closed-loop system," in Proc. IEEE Int. Conf. Fuzzy Systems, Barcelona, Spain, 1997, pp. 185-192.
14. M. Johansson, A. Rantzer, and K.-E. Arzen, "Piecewise quadratic stability of fuzzy systems," IEEE Trans. Fuzzy Syst., vol. 7, no. 6, pp. 713-722, Dec. 1999.
15. F. Cuesta, F. Gordillo, J. Aracil, and A. Ollero, "Stability analysis of nonlinear multivariable Takagi-Sugeno fuzzy control systems," IEEE Trans. Fuzzy Syst., vol. 7, no. 5, pp. 508-520, Oct. 1999.
16. S. Boyd, L. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.
17. P. Bergsten, R. Palm, and D. Driankov, "Observers for Takagi-Sugeno fuzzy systems," IEEE Trans. Syst., Man, Cybern B, Cybern., vol. 32, no. 1, pp. 114-121, Feb. 2001.
18. ∞ nonlinear control via fuzzy static output feedback," IEEE Trans. Circuits Syst. I, vol. 50, no. 11, pp. 1494-1502, Nov. 2003.
19. L.-X. Wang, A Course in Fuzzy Systems and Control. Upper Saddle River, NJ: Prentice-Hall, 1997.
20. K.-H. Kim and M.-J. Yoon, "A nonlinear speed control for a PM synchronous motor using a simple disturbance estimation technique," IEEE Trans. Ind. Electron., vol. 49, no. 3, pp. 524-535, Jun. 2002.
21. J. E. Slotine and W. Li, Applied Nonlinear Control. Upper Saddle River: Prentice-Hall, 1991.