Enlarging the Domain of Attraction in Nonlinear Polynomial Systems

Authors

  • Faiçal Hamidi Unite de Recherche Modelisation, Analyse et Commande des Systemes, ENIG, 6029 Gabes, Tunisie.
  • Houcem Jerbi Laboratoire d'Etude et de Commande Automatique des Processus (LECAP) Ecole Polytechnique de Tunisie BP 748-2078 La Marsa-Tunisie.
  • Wahida Aggoune Equipe Commande des Systemes (ECS), ENSEA,6 avenue du Ponceau, 95014 Cergy-Pontoise Cedex, France.
  • Mohamed DJEMAI University of Valenciennes
  • Mohamed Naceur Abdelkrim Unite de Recherche Modelisation, Analyse et Commande des Systemes, ENIG, 6029 Gabes, Tunisie

Keywords:

Nonlinear Polynomial Systems, LMI, Genetic Algorithm, Stability

Abstract

This paper addresses the problem of enlarging the Domain of Attraction (DA)  based on a Generalized Eigenvalue Problem (GEVP)  approach. The main contribution of the present development is the maximization of the (DA)  while characterizing the asymptotic stability region by a Lyapunov Function. Such result is obtained using a Genetic Algorithm (GA) . A theoretical proof of the validity of the obtained domain is developed. An illustrative example ends the paper.

Author Biography

Mohamed DJEMAI, University of Valenciennes

LAMIH-Laboratory, CNRS UMR 8201Laboratory of Industrial and Human Automation, Mechanics and Computer Science ASHM -Group. - Automatic Control and Human-Machine SystemsUVHC, Le Mont Houy, Malvache Building59313 Valenciennes Cedex 9 

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Published

2013-08-01

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