# Patchy Vector Fields and Asymptotic Stabilization

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 4, page 445-471
- ISSN: 1292-8119

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topAncona, Fabio, and Bressan, Alberto. "Patchy Vector Fields and Asymptotic Stabilization." ESAIM: Control, Optimisation and Calculus of Variations 4 (2010): 445-471. <http://eudml.org/doc/116552>.

@article{Ancona2010,

abstract = {
This paper is concerned with the structure of
asymptotically
stabilizing feedbacks for a nonlinear control system
on $\mathbb\{R\}^n$.
We first introduce a family of discontinuous, piecewise smooth vector fields
and derive a number of properties enjoyed by
solutions of the corresponding O.D.E's.
We then define a class of “patchy feedbacks”
which are obtained by patching together a locally finite
family of smooth controls.
Our main result shows that,
if a system is asymptotically controllable at the origin, then
it can be stabilized by a piecewise constant
patchy feedback control.
},

author = {Ancona, Fabio, Bressan, Alberto},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {
Asymptotic controllability;
feedback asymptotic stabilization;
discontinuous feedback; discontinuous vector fields.
; asymptotic controllability; feedback asymptotic stabilization; discontinuous feedback; discontinuous vector fields},

language = {eng},

month = {3},

pages = {445-471},

publisher = {EDP Sciences},

title = {Patchy Vector Fields and Asymptotic Stabilization},

url = {http://eudml.org/doc/116552},

volume = {4},

year = {2010},

}

TY - JOUR

AU - Ancona, Fabio

AU - Bressan, Alberto

TI - Patchy Vector Fields and Asymptotic Stabilization

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 4

SP - 445

EP - 471

AB -
This paper is concerned with the structure of
asymptotically
stabilizing feedbacks for a nonlinear control system
on $\mathbb{R}^n$.
We first introduce a family of discontinuous, piecewise smooth vector fields
and derive a number of properties enjoyed by
solutions of the corresponding O.D.E's.
We then define a class of “patchy feedbacks”
which are obtained by patching together a locally finite
family of smooth controls.
Our main result shows that,
if a system is asymptotically controllable at the origin, then
it can be stabilized by a piecewise constant
patchy feedback control.

LA - eng

KW -
Asymptotic controllability;
feedback asymptotic stabilization;
discontinuous feedback; discontinuous vector fields.
; asymptotic controllability; feedback asymptotic stabilization; discontinuous feedback; discontinuous vector fields

UR - http://eudml.org/doc/116552

ER -

## References

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