Non-quadratic performance design for Takagi-Sugeno fuzzy systems

Miguel Bernal; Petr Hušek

International Journal of Applied Mathematics and Computer Science (2005)

  • Volume: 15, Issue: 3, page 383-391
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Bernal, Miguel, and Hušek, Petr. "Non-quadratic performance design for Takagi-Sugeno fuzzy systems." International Journal of Applied Mathematics and Computer Science 15.3 (2005): 383-391. <http://eudml.org/doc/207752>.

@article{Bernal2005,
abstract = {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.},
author = {Bernal, Miguel, Hušek, Petr},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {fuzzy control; Lyapunov functions; LMIs; LMI},
language = {eng},
number = {3},
pages = {383-391},
title = {Non-quadratic performance design for Takagi-Sugeno fuzzy systems},
url = {http://eudml.org/doc/207752},
volume = {15},
year = {2005},
}

TY - JOUR
AU - Bernal, Miguel
AU - Hušek, Petr
TI - Non-quadratic performance design for Takagi-Sugeno fuzzy systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2005
VL - 15
IS - 3
SP - 383
EP - 391
AB - 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.
LA - eng
KW - fuzzy control; Lyapunov functions; LMIs; LMI
UR - http://eudml.org/doc/207752
ER -

References

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  1. 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. 
  2. 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. 
  3. 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. 
  4. 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. 
  5. 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. Zbl1169.93355
  6. 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. 
  7. 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. 
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  15. Tanaka K. and Wang H. O. (2001): Fuzzy Control Systems Design and Analysis. - New York: Wiley . 
  16. 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. 
  17. 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. 
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