Stability Rates for Patchy Vector Fields

Details Stability Rates for Patchy Vector Fields Stability Rates for Patchy Vector Fields

2001-11-09

arxiv.org/abs/math/0111109v1

Mathematics

Optimization and Control

37 pages, 2 figures

Scientific paper

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.

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