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Mathematical Problems in Engineering
Volume 8, Issue 3, Pages 221-231

Study of the stability of fuzzy controllers by an estimation of the attraction regions: A Vector Norm approach

1Institut Agro-Alimentaire de Lille, LAIL UPRES A CNRS 8021, Cite Scientifique, Villeneuve d'Ascq 59655, France
2Ecole Centrale de Lille , LAIL UPRES A CNRS 8021, Cite Scientifique, Villeneuve d'Ascq 59655, France

Received 3 August 2000; Revised 10 September 2001

Copyright © 2002 Hindawi Publishing Corporation. 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.


A fuzzy controller with singleton defuzzification can be considered as the association of a regionwise constant term and of a regionwise non linear term, the latter being bounded by a linear controller. Based on the regionwise structure of fuzzy controller, the state space is partitioned into a series of disjoint sets. The fuzzy controller parameters are tuned in order to ensure that the ith set is included into the domain of attraction of the preceding sets of the series. If the first set of the series is included into the region of attraction of the equilibrium point, the overall fuzzy controlled system is stable. The attractors are estimated with the help of the comparison principle, using Vector Norms, which ensures the robustness with respect to uncertainties and perturbations of the open loop system.