Stability rates for patchy vector fields

Fabio Ancona; Alberto Bressan

doi:10.1051/cocv:2004003

Stability rates for patchy vector fields

Fabio Ancona, Alberto Bressan

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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.

Original language	English (US)
Pages (from-to)	168-200
Number of pages	33
Journal	ESAIM - Control, Optimisation and Calculus of Variations
Volume	10
Issue number	2
DOIs	https://doi.org/10.1051/cocv:2004003
State	Published - Apr 2004

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Control and Optimization
Computational Mathematics

Access to Document

10.1051/cocv:2004003

Cite this

@article{42c1313d71c0410687b533bae2860799,

title = "Stability rates for patchy vector fields",

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.",

author = "Fabio Ancona and Alberto Bressan",

year = "2004",

month = apr,

doi = "10.1051/cocv:2004003",

language = "English (US)",

volume = "10",

pages = "168--200",

journal = "ESAIM - Control, Optimisation and Calculus of Variations",

issn = "1292-8119",

publisher = "EDP Sciences",

number = "2",

}

TY - JOUR

T1 - Stability rates for patchy vector fields

AU - Ancona, Fabio

AU - Bressan, Alberto

PY - 2004/4

Y1 - 2004/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=12844283926&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=12844283926&partnerID=8YFLogxK

U2 - 10.1051/cocv:2004003

DO - 10.1051/cocv:2004003

M3 - Article

AN - SCOPUS:12844283926

SN - 1292-8119

VL - 10

SP - 168

EP - 200

JO - ESAIM - Control, Optimisation and Calculus of Variations

JF - ESAIM - Control, Optimisation and Calculus of Variations

IS - 2

ER -

Stability rates for patchy vector fields

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this