no. 2
Stability rates for patchy vector fields
ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 2, pp. 168-200.

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.

DOI : 10.1051/cocv:2004003
Classification : 34A37, 34D, 93D09, 93D15
Mots clés : Patchy vector field, impulsive perturbation 
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     title = {Stability rates for patchy vector fields},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
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     publisher = {EDP-Sciences},
     volume = {10},
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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. http://www.numdam.org/articles/10.1051/cocv:2004003/

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