Enlarging the Domain of Attraction in Nonlinear Polynomial Systems

  • 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

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
How to Cite
HAMIDI, Faiçal et al. Enlarging the Domain of Attraction in Nonlinear Polynomial Systems. INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL, [S.l.], v. 8, n. 4, p. 538-547, aug. 2013. ISSN 1841-9844. Available at: <http://univagora.ro/jour/index.php/ijccc/article/view/152>. Date accessed: 06 aug. 2020. doi: https://doi.org/10.15837/ijccc.2013.4.152.

Keywords

Nonlinear Polynomial Systems, LMI, Genetic Algorithm, Stability