Non-quadratic performance design for Takagi-Sugeno fuzzy systems
Bernal, Miguel ; Hušek, Petr
International Journal of Applied Mathematics and Computer Science, Tome 15 (2005), p. 383-391 / Harvested from The Polish Digital Mathematics Library
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This paper improves controller synthesis of discrete Takagi-Sugeno fuzzy systems based on non-quadratic Lyapunov functions, making it possible to accomplish various kinds of control performance specifications such as decay rate conditions, requirements on control input and output and disturbance rejection. These extensions can be implemented via linear matrix inequalities, which are numerically solvable with commercially available software. The controller design is illustrated with an example.

Publié le : 2005-01-01
EUDML-ID : urn:eudml:doc:207752 
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     title = {Non-quadratic performance design for Takagi-Sugeno fuzzy systems},
     journal = {International Journal of Applied Mathematics and Computer Science},
     volume = {15},
     year = {2005},
     pages = {383-391},
     zbl = {1169.93355},
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Bernal, Miguel; Hušek, Petr. Non-quadratic performance design for Takagi-Sugeno fuzzy systems. International Journal of Applied Mathematics and Computer Science, Tome 15 (2005) pp. 383-391. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv15i3p383bwm/

[000] Bernal M. and Hušek P. (2004a): Piecewise quadratic stability of parallel-distributed compensatedi Takagi-Sugeno fuzzy systems. - Proc. Int. Conf. Methods and Models inAutomation and Robotics, Międzyzdroje, Poland, pp. 1417-1422.

[001] Bernal M. and Hušek P. (2004b): Piecewise quadratic stability of affine Takagi-Sugeno fuzzy control systems. - Proc. Advanced Fuzzy-Neural Control Conference, Oulu, Finland, pp. 157-162.

[002] Bernal M. and Hušek P. (2004c): Piecewise Quadratic Stability of Discrete-time Takagi-Sugeno Fuzzy Systems. - Proc. 2nd IFAC Symp. Syst., Structure and Control, Oaxaca, Mexico, pp. 771-775.

[003] Bernal M. and Hušek P. (2005a): Decay rate fuzzy controller design with piecewise Lyapunov functions. - Proc. 24th IASTED Int. Conf. Modeling, Identification and Control, Innsbruck, Austria, on CD-ROM.

[004] Bernal M. and Hušek P. (2005b): Controller synthesis with input and output constraints for fuzzy systems. - Proc. 16th IFAC World Congress, Prague, Czech Republic, on DVD-ROM. | Zbl 1169.93355

[005] Bernal M. and Hušek P. (2005c): Non-quadratic discrete fuzzy controller design performing decayrate. - Proc. Int. Conf. FUZZ-IEEE, Reno, U.S.A., on CD-ROM.

[006] Farinwata S. S. and Vachtsevanos G. (1993): Stability analysis of the fuzzy logic controller. - Proc. IEEE CDC, San Antonio, U.S.A., pp. 1377-1382.

[007] Feng, G. (2003): Controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions. - IEEE Trans. Fuzzy Syst., Vol. 11, pp. 605-612.

[008] Feng G. (2004): Stability analysis of discrete time fuzzy dynamic systems based on piecewise Lyapunov functions. - IEEE Trans. Fuzzy Syst.,Vol. 12, pp. 22-28.

[009] Guerra T.M. and Vermeiren L. (2004): LMI-based relaxed non-quadratic stabilization conditions for nonlinear systems in Takagi-Sugeno's form. - Automatica, Vol. 40, pp. 823-829. | Zbl 1050.93048

[010] Johansson M., Rantzer A. and Arzen K. (1999): Piecewise quadratic stability of fuzzy systems. - IEEE Trans. Fuzzy Syst., Vol. 7, pp. 713-722.

[011] Rantzer A. and Johansson M. (2000): Piecewise linear quadratic optimal control. - IEEE Trans. Automat. Contr., Vol. 45, pp. 629-637. | Zbl 0969.49016

[012] Tanaka K., Hori T. and Wang H.O.(2003): Amultiple function approach to stabilization of fuzzy control systems. - IEEE Trans. Fuzzy Syst., Vol. 11, pp. 582-589.

[013] Takagi T. and Sugeno M. (1985): Fuzzy identification of systems and its applications to modeling and control. - IEEE Trans.Syst., Man Cybern., Vol. 15, pp. 116-132. | Zbl 0576.93021

[014] Tanaka K. and Wang H. O. (2001): Fuzzy Control Systems Design and Analysis. - New York: Wiley .

[015] Tanaka K. and Sano M. (1994): 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, pp. 119-134.

[016] Tanaka K. and Sugeno M. (1990): Stability analysis of fuzzy systems using Lyapunov's direct method. - Proc. North American Fuzzy Information Processing Society (NAFIPS'90), Canada: Toronto, pp. 133-136.

[017] Tanaka K. and Sugeno M. (1992): Stability analysis and design of fuzzy control systems. - Fuzzy Sets Syst., Vol. 45,No. 2, pp. 135-156. | Zbl 0758.93042

[018] Tanaka K., Ikeda T. and Wang H. O. (1998): Fuzzy regulators and fuzzy observers: Relaxed stability conditions and LMI-based designs. - IEEE Trans. Fuzzy Syst.,Vol. 6, pp. 250-264.

[019] Wang H. O., Tanaka K. and Griffin M. (1996): An approach to fuzzy control of nonlinear systems: Stability and design issues. - IEEE Trans. Fuzzy Syst., Vol. 4, pp. 14-23.