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

El Hajjaji, A.; Benzaouia, A.; Naib, M.

doi:https://doi.org/10.1155/MPE/2006/13832

Mathematical Problems in Engineering

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Volume 2006 | Article ID 013832 | https://doi.org/10.1155/MPE/2006/13832

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

A. El Hajjaji,¹A. Benzaouia,²and M. Naib²

Received11 Jun 2005

Revised10 Apr 2006

Accepted28 Apr 2006

Published11 Jul 2006

Abstract

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.

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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.

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