Geodesic
Homogeneous approximations and local observer design
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 3, pp. 906-929

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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.

DOI : 10.1051/cocv/2012038
Classification : 93B07, 93B29, 16W25
Keywords: homogeneity, approximations, local observer 
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     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://geodesic.mathdoc.fr/articles/10.1051/cocv/2012038/}
}
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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

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