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Mathematical Problems in Engineering
Volume 2006, Article ID 43681, 28 pages

Lyapunov-Schmidt method dedicated to the observer analysis and design

1Département de Mathématique et d'Informatique, Institut de Mathèmatique, Université Abou Bekr Belkaid Tlemcen, BP 119, Tlemcen 13000, Algeria
2Equipe Commande des Systèmes (ECS)-EA 3649, ENSEA, 6 Avenue du Ponceau, Cergy-Pontoise Paris 95014, France

Received 14 June 2005; Revised 14 February 2006; Accepted 5 March 2006

Copyright © 2006 D. Benmerzouk and J. P. Barbot. 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.


An analysis of observation error dynamics and an observer design are presented using the so-called Lyapunov-Schmidt method, firstly in order to analyze the solution's bifurcation of the observation error dynamics, and secondly in order to propose a robust observer with respect to such solution's bifurcation. Two numerical examples based on the Galerkin method show the pertinence of the proposed approach.