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.
Mots-clés : homogeneity, approximations, local observer
@article{COCV_2013__19_3_906_0,
author = {M\'enard, Tomas and Moulay, Emmanuel and Perruquetti, Wilfrid},
title = {Homogeneous approximations and local observer design},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {906--929},
publisher = {EDP-Sciences},
volume = {19},
number = {3},
year = {2013},
doi = {10.1051/cocv/2012038},
mrnumber = {3092367},
zbl = {1269.93015},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2012038/}
}
TY - JOUR AU - Ménard, Tomas AU - Moulay, Emmanuel AU - Perruquetti, Wilfrid TI - Homogeneous approximations and local observer design JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 906 EP - 929 VL - 19 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2012038/ DO - 10.1051/cocv/2012038 LA - en ID - COCV_2013__19_3_906_0 ER -
%0 Journal Article %A Ménard, Tomas %A Moulay, Emmanuel %A Perruquetti, Wilfrid %T Homogeneous approximations and local observer design %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 906-929 %V 19 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2012038/ %R 10.1051/cocv/2012038 %G en %F COCV_2013__19_3_906_0
Ménard, Tomas; Moulay, Emmanuel; Perruquetti, Wilfrid. Homogeneous approximations and local observer design. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 3, pp. 906-929. doi : 10.1051/cocv/2012038. http://archive.numdam.org/articles/10.1051/cocv/2012038/
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