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Stability rates for patchy vector fields

Published online by Cambridge University Press:  15 March 2004

Fabio Ancona  and
Alberto Bressan
Fabio Ancona
Affiliation:
Dipartimento di Matematica and C.I.R.A.M., Università di Bologna, Piazza Porta S. Donato 5, Bologna 40127, Italy; ancona@ciram.unibo.it.
Alberto Bressan
Affiliation:
S.I.S.S.A., Via Beirut 4, Trieste 34014, Italy; bressan@sissa.it.
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Abstract

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.

Keywords

Patchy vector fieldimpulsive perturbation.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 10 , Issue 2 , April 2004 , pp. 168 - 200
Copyright
© EDP Sciences, SMAI, 2004

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References

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