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Stability rates for patchy vector fields. (English) Zbl 1083.34037
The stability of a set of trajectories of a patchy vector field in the presence of impulsive perturbations is studied. Patchy vector fields are discontinuous, piecewise smooth vector fields to study feedback stabilization problems. They were introduced by the authors [ESAIM, Control Optim. Calc. Var. 4, 445–471 (1999; Zbl 0924.34058)]. For patchy vector fields in the plane with polygonal patches in generic position, it is shown that the distance between a perturbed trajectory and an unperturbed one is of the same order of magnitude as that of the impulsive forcing term.

MSC:
34D20 Stability of solutions to ordinary differential equations
34A37 Ordinary differential equations with impulses
34A36 Discontinuous ordinary differential equations
93D09 Robust stability
93D15 Stabilization of systems by feedback
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