2001/11/09 by Fabio Ancona, Alberto Bressan, Ancona, Fabio +1
Engineering · Mathematics · #34 A #34 D #49 E #93 D #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Nonlinear Differential Equations Analysis #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #math.OC #msc:34 #msc:49 #msc:93
paper · pdf · doi:10.48550/arxiv.math/0111109
37 pages, 2 figures
arxiv created 2001/11/09 · openalex publication_date 2001/11/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper is concerned with the stability of the set of trajectories of a vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in AB 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.