On Improvement of Stability Conditions for Continuous Mamdani-Like Fuzzy Systems

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

Volumn 34, Issue 1, 2004, Pages 120-131

  Sugeno, Michio ^a   Taniguchi, Tadanari ^a  

^a Brain Science Institute   (Japan)

Author keywords

Canonical form; Necessary and sufficient conditions; Quadratic stability; Type II fuzzy system

Indexed keywords

APPROXIMATION THEORY; FEEDBACK CONTROL; FUNCTIONS; FUZZY SETS; LINEAR SYSTEMS; LYAPUNOV METHODS; MATRIX ALGEBRA; SYSTEM STABILITY; THEOREM PROVING; VECTORS;

CANONICAL FORMS; NECESSARY AND SUFFICIENT CONDITIONS; QUADRATIC STABILITY; TYPE II FUZZY SYSTEM;

FUZZY CONTROL;

EID: 0742307299     PISSN: 10834419     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSMCB.2003.809226     Document Type: Article

References (22)

1. E. H. Mamdani and S. Assilian, "An experiment in linguistic synthesis with a fuzzy logic controller," Int. J. Man-Mach. Stud., vol. 7, pp. 1-13, 1975.
2. M. Braae and D. A. Rutherford, "Theoretical and linguistic aspects of the fuzzy logic controller," Automatica, vol. 15, pp. 553-577, 1979.
3. M. Sugeno and T. Takagi, "A new approach to design of fuzzy controller," in Advances in Fuzzy Sets and Possibility Theory, and Applications, P. P. Wang, Ed. New York: Plenum, 1983.
4. K. S. Ray and D. D. Majumder, "Application of circle criteria for stability analysis of linear SISO and MIMO system associated with fuzzy logic Controller," IEEE Trans. Syst., Man, Cybern., vol. SMC-14, pp. 345-349, 1984.
5. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its application to modeling and control," IEEE Trans. Syst., Man, Cybern., vol. SMC-15, pp. 116-132, 1985.
6. K. Tanaka and M. Sugeno, "Stability analysis of fuzzy systems using Lyapunov's direct method," in Proc. North Amer. Fuzzy Ingorm. Processing Soc. (NAFIPS), New York, June 1990, pp. 133-136.
7. J. Aracil, A. Garcia-Cerezo, A. Barreiro, and A. Ollero, "Fuzzy control of dynamical systems, and stability analysis based on the conicity criterion," in Proc. IFSA World Congr., Brussels, Belgium, July 1991, pp. 5-8.
8. R. Katoh, T. Yamashita, and S. Singh, "Stability analysis of control system having PD type of fuzzy controller," Fuzzy Sets Syst., vol. 74, pp. 321-334, 1995.
9. T. Hasegawa, T. Furuhashi, and Y. Uchikawa, "On design of fuzzy controllers using fuzzy models and modifications of control rules based on descriptions of dynamical behavior of control systems," J. Jpn. Soc. Fuzzy Theory Syst., vol. 7, no. 2, pp. 413-431, 1995.
10. S. Galichet and L. Foulloy, "Fuzzy controllers: synthesis and equivalences," IEEE Trans. Fuzzy Syst., vol. 3, pp. 140-148, May 1995.
11. H. O. Wang, K. Tanaka, and M. F. Griffin, "An approach to fuzzy control of nonlinear systems: Stability and design issues," IEEE Trans. Fuzzy Syst., vol. 4, pp. 14-23, Feb. 1996.
12. L. T. Kóczy, "Fuzzy if . . . then rule models and their transformation into one another," IEEE Trans. Syst., Man, Cybern., vol. 26, pp. 621-637, Sept. 1996.
13. P.-Z. Wang, S. Ten, F. Song, and P. Liang, "Constructive theory for fuzzy systems," Fuzzy Sets Syst., vol. 88, pp. 195-203, 1997.
14. K. Tanaka, T. Ikeda, and H. O. Wang, "An LMI approach to fuzzy controller designs based on relaxed stability conditions," in Proc. 6th IEEE Int. Conf. Fuzzy Syst., Barcelona, Spain, July 1997, pp. 171-176.
15. M. Sugeno and C.-H. Lee, "Stabilizing control of fuzzy systems with singleton consequents," J. Jpn. Soc. Fuzzy Theory Syst., vol. 10, pp. 915-936, 1998. Japanese.
16. M. Sugeno, "On stability of fuzzy systems expressed by fuzzy rules with singleton consequents," IEEE Trans. Fuzzy Syst., vol. 7, pp. 201-224, Apr. 1999.
17. C.-H. Lee and M. Sugeno, "Stability conditions for closed-loop fuzzy systems with singleton consequents," in Proc. 1999 IEEE Int. Conf. Fuzzy Syst., Seoul, Korea, Aug. 1999, pp. I-263-I-268.
18. _, "A construction procedure of a Lyapunov function in stability analysis of fuzzy systems with singleton consequents," in Proc. 1999 IEEE Int. Conf. Systems, Man, and Cybernetics, Tokyo, Japan, Oct. 1999, pp. III-1-III-6.
19. C.-H. Lee, "Stability Analysis and Stabilization of Fuzzy Systems With Singleton Consequents," Ph.D. dissertation, Tokyo Inst. Technol., Tokyo, Japan, 1999.
20. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.
21. R. Sepulchre, M. Janković, and P. Kokotović, Constructive Nonlinear Control. New York: Springer, 1997.
22. T. L. Vincent and W. J. Grantham, Nonlinear and Optimal Control Systems. New York: Wiley, 1997.