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Mathematical Problems in Engineering
Volume 2006, Article ID 13832, 17 pages

Stabilization of fuzzy systems with constrained controls by using positively invariant sets

1Centre de Robotique, d'Electrotechnique, et d'Automatique, Université de Picardie, 7 Rue du Moulin Neuf, Picardie, Amiens 80 000, France
2Equipe d'Automatique et de Contrôle des Procédés Industriels, Departement Physique, Faculte des Sciences Semlalia Marrakech, L'Université Cadi Ayyad, BP 2390, Marrakech 40001, Morocco

Received 11 June 2005; Revised 10 April 2006; Accepted 28 April 2006

Copyright © 2006 A. El Hajjaji et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We deal with the extension of the positive invariance approach to nonlinear systems modeled by Takagi-Sugeno fuzzy systems. The saturations on the control are taken into account during the design phase. Sufficient conditions of asymptotic stability are given ensuring at the same time that the control is always admissible inside the corresponding polyhedral set. Both a common Lyapunov function and piecewise Lyapunov function are used.