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This paper is concerned with the stability of the set of trajectories of a patchy vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in Ancona and Bressan (1999) to study feedback stabilization problems. For patchy vector fields in the plane, with polygonal patches in generic position, we show that the distance between a perturbed trajectory and an unperturbed one is of the same order of magnitude as the impulsive forcing term.
@article{COCV_2004__10_2_168_0,
author = {Ancona, Fabio and Bressan, Alberto},
title = {Stability rates for patchy vector fields},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {168--200},
publisher = {EDP-Sciences},
volume = {10},
number = {2},
year = {2004},
doi = {10.1051/cocv:2004003},
mrnumber = {2083482},
zbl = {1083.34037},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2004003/}
}
TY - JOUR AU - Ancona, Fabio AU - Bressan, Alberto TI - Stability rates for patchy vector fields JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2004 SP - 168 EP - 200 VL - 10 IS - 2 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2004003/ DO - 10.1051/cocv:2004003 LA - en ID - COCV_2004__10_2_168_0 ER -
%0 Journal Article %A Ancona, Fabio %A Bressan, Alberto %T Stability rates for patchy vector fields %J ESAIM: Control, Optimisation and Calculus of Variations %D 2004 %P 168-200 %V 10 %N 2 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2004003/ %R 10.1051/cocv:2004003 %G en %F COCV_2004__10_2_168_0
Ancona, Fabio; Bressan, Alberto. Stability rates for patchy vector fields. ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 2, pp. 168-200. doi: 10.1051/cocv:2004003
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