Mathematical Problems in Engineering

Mathematical Problems in Engineering / 2002 / Article

Open Access

Volume 8 |Article ID 465328 |

J.-Y. Dieulot, A. El Kamel, P. Borne, "Study of the stability of fuzzy controllers by an estimation of the attraction regions: A Vector Norm approach", Mathematical Problems in Engineering, vol. 8, Article ID 465328, 11 pages, 2002.

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

Received03 Aug 2000
Revised10 Sep 2001


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.

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.

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