Homogeneous approximations and local observer design

¹ GREYC, UMR CNRS 6072, Université de Caen, 6 Bd du Maréchal Juin, BP 5186–14032 Caen Cedex, France
tomas.menard@unicaen.fr
² Xlim-SIC, UMR CNRS 6172, Université de Poitiers, Bvd Marie et Pierre Curie, BP 30179, 86962 futuroscope Chasseneuil, France
emmanuel.moulay@univ-poitiers.fr
³ NON-A, INRIA Lille Nord Europe and LAGIS UMR CNRS 8219, Ecole Centrale de Lille, BP 48, 59651 Villeneuve D’Ascq, France
wilfrid.perruquetti@ec-lille.fr

Received: 10 April 2012
Revised: 25 September 2012

Abstract

This paper is concerned with the construction of local observers for nonlinear systems without inputs, satisfying an observability rank condition. The aim of this study is, first, to define an homogeneous approximation that keeps the observability property unchanged at the origin. This approximation is further used in the synthesis of a local observer which is proven to be locally convergent for Lyapunov-stable systems. We compare the performance of the homogeneous approximation observer with the classical linear approximation observer on an example.