Nonquadratic stabilization of continuous-time systems in the Takagi-Sugeno form

Miguel Bernal; Petr Hušek; Vladimír Kučera

Kybernetika (2006)

  • Volume: 42, Issue: 6, page 665-672
  • ISSN: 0023-5954

Abstract

top
This paper presents a relaxed scheme for controller synthesis of continuous- time systems in the Takagi-Sugeno form, based on non-quadratic Lyapunov functions and a non-PDC control law. The relaxations here provided allow state and input dependence of the membership functions’ derivatives, as well as independence on initial conditions when input constraints are needed. Moreover, the controller synthesis is attainable via linear matrix inequalities, which are efficiently solved by commercially available software.

How to cite

top

Bernal, Miguel, Hušek, Petr, and Kučera, Vladimír. "Nonquadratic stabilization of continuous-time systems in the Takagi-Sugeno form." Kybernetika 42.6 (2006): 665-672. <http://eudml.org/doc/33831>.

@article{Bernal2006,
abstract = {This paper presents a relaxed scheme for controller synthesis of continuous- time systems in the Takagi-Sugeno form, based on non-quadratic Lyapunov functions and a non-PDC control law. The relaxations here provided allow state and input dependence of the membership functions’ derivatives, as well as independence on initial conditions when input constraints are needed. Moreover, the controller synthesis is attainable via linear matrix inequalities, which are efficiently solved by commercially available software.},
author = {Bernal, Miguel, Hušek, Petr, Kučera, Vladimír},
journal = {Kybernetika},
keywords = {fuzzy models; nonquadratic stabilization; nonlinear control; Lyapunov function; linear matrix inequality (LMI); fuzzy model; nonquadratic stabilization; nonlinear control; Lyapunov function; linear matrix inequality (LMI)},
language = {eng},
number = {6},
pages = {665-672},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Nonquadratic stabilization of continuous-time systems in the Takagi-Sugeno form},
url = {http://eudml.org/doc/33831},
volume = {42},
year = {2006},
}

TY - JOUR
AU - Bernal, Miguel
AU - Hušek, Petr
AU - Kučera, Vladimír
TI - Nonquadratic stabilization of continuous-time systems in the Takagi-Sugeno form
JO - Kybernetika
PY - 2006
PB - Institute of Information Theory and Automation AS CR
VL - 42
IS - 6
SP - 665
EP - 672
AB - This paper presents a relaxed scheme for controller synthesis of continuous- time systems in the Takagi-Sugeno form, based on non-quadratic Lyapunov functions and a non-PDC control law. The relaxations here provided allow state and input dependence of the membership functions’ derivatives, as well as independence on initial conditions when input constraints are needed. Moreover, the controller synthesis is attainable via linear matrix inequalities, which are efficiently solved by commercially available software.
LA - eng
KW - fuzzy models; nonquadratic stabilization; nonlinear control; Lyapunov function; linear matrix inequality (LMI); fuzzy model; nonquadratic stabilization; nonlinear control; Lyapunov function; linear matrix inequality (LMI)
UR - http://eudml.org/doc/33831
ER -

References

top
  1. Apkarian X., Gahinet X., A convex characterization of gain scheduling Hinf controllers, IEEE Trans. Control Systems 40 (1995), 853–864 (1995) MR1328081
  2. Begovich O., Sanchez E. N., Maldonado M., 10.1109/87.974334, IEEE Trans. Control Systems Techn. 10 (2002), 14–20 DOI10.1109/87.974334
  3. Bernal M., Hušek P., Piecewise quadratic stability of affine Takagi–Sugeno fuzzy control systems, In: Proc. Advanced Fuzzy-Neural Control Conference, Oulu 2004, pp.157–162 
  4. Bernal M., Hušek P., Controller synthesis with input and output constraints for fuzzy systems, In: 16th IFAC World Congress DVD-edition, Prague 2005 
  5. Bernal M., Non-quadratic discrete fuzzy controller design performing decay rate, In: FUZZ–IEEE Internat. Conference, Reno 2005, CD edition 
  6. Bernal M., Hušek, P., Kučera V., Non-quadratic design for continuous-time systems in the Takagi–Sugeno form, Submitted to Automatica 
  7. Feng G., 10.1109/TFUZZ.2003.817837, IEEE Trans. Fuzzy Systems 11 (2003), 605–612 DOI10.1109/TFUZZ.2003.817837
  8. Feng G., 10.1109/TFUZZ.2003.819833, IEEE Trans. Fuzzy Systems 12 (2004), 22–28 DOI10.1109/TFUZZ.2003.819833
  9. Guerra T. M., Vermeiren L., 10.1016/j.automatica.2003.12.014, Automatica 40 (2004), 823–829 MR2152188DOI10.1016/j.automatica.2003.12.014
  10. Johansson M., Rantzer, A., Arzen K., 10.1109/91.811241, IEEE Trans. Fuzzy Systems 7 (1999), 713–722 (1999) DOI10.1109/91.811241
  11. Rantzer A., Johansson M., 10.1109/9.847100, IEEE Trans. Automat. Control 45 (2000), 629–637 Zbl0969.49016MR1764832DOI10.1109/9.847100
  12. Takagi T., Sugeno M., 10.1109/TSMC.1985.6313399, IEEE Trans. Systems, Man and Cybernet. 15 (1985), 116–132 (1985) Zbl0576.93021DOI10.1109/TSMC.1985.6313399
  13. Tanaka K., Sugeno M., Stability analysis of fuzzy systems using Lyapunov’s direct method, In: Proc. NAFIPS’90, pp. 133–136 
  14. Tanaka K., Ikeda, T., Wang H. O., 10.1109/91.669023, IEEE Trans. Fuzzy Systems 6 (1998), 250–264 (1998) DOI10.1109/91.669023
  15. Tanaka K., Hori, T., Wang H. O., 10.1109/TFUZZ.2003.814861, IEEE Trans. Fuzzy Systems 11 (2003), 582–589 DOI10.1109/TFUZZ.2003.814861
  16. H. O. Wang, Tanaka, K., Griffin M., 10.1109/91.481841, IEEE Trans. Fuzzy Systems 4 (1996), 14–23 (1996) DOI10.1109/91.481841

NotesEmbed ?

top

You must be logged in to post comments.