Mathematical Problems in Engineering 
Volume 2004 (2004), Issue 1, Pages 11-31
doi:10.1155/S1024123X04309038

Sliding mode observers and observability singularity in chaotic synchronization

L. Boutat-Baddas,1 J. P. Barbot,1 D. Boutat,2 and R. Tauleigne1

 1Equipe Commande des Systèmes, École Nationale Supérieure de l'Electronique et de ses Applications, 6 avenue du Ponceau, Cergy Cedex 95014, France
2Laboratoire Vision et Robotique, École Nationale Supérieure d'Ingenieurs de Bourges et Université d'Orléans, 10 Boulevard Lahitolle, Bourges Cedex 18020, France
Received 29 September 2003; Revised 28 January 2004

Abstract

We present a new secured data transmission based on a chaotic synchronization and observability singularity. For this, we adopt an approach based on an inclusion of the message in the system structure and we use a sliding mode observer for system with unknown input in order to recover the information. We end the paper with an example of chaotic system with an observability bifurcation. Moreover, this example highlights some benefits of the so-called step-by-step sliding mode observer.