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

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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

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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

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  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
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