Stability rates for patchy vector fields
ESAIM: Control, Optimisation and Calculus of Variations (2010)
- Volume: 10, Issue: 2, page 168-200
- ISSN: 1292-8119
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topAncona, Fabio, and Bressan, Alberto. "Stability rates for patchy vector fields." ESAIM: Control, Optimisation and Calculus of Variations 10.2 (2010): 168-200. <http://eudml.org/doc/90724>.
@article{Ancona2010,
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 = {Ancona, Fabio, Bressan, Alberto},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Patchy vector field; impulsive perturbation.; patchy vector field; impulsive perturbation},
language = {eng},
month = {3},
number = {2},
pages = {168-200},
publisher = {EDP Sciences},
title = {Stability rates for patchy vector fields},
url = {http://eudml.org/doc/90724},
volume = {10},
year = {2010},
}
TY - JOUR
AU - Ancona, Fabio
AU - Bressan, Alberto
TI - Stability rates for patchy vector fields
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 10
IS - 2
SP - 168
EP - 200
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.
LA - eng
KW - Patchy vector field; impulsive perturbation.; patchy vector field; impulsive perturbation
UR - http://eudml.org/doc/90724
ER -
References
top- F. Ancona and A. Bressan, Patchy vector fields and asymptotic stabilization. ESAIM: COCV4 (1999) 445-471.
- F. Ancona and A. Bressan, Flow Stability of Patchy vector fields and Robust Feedback Stabilization. SIAM J. Control Optim.41 (2003) 1455-1476.
- A. Bressan, On differential systems with impulsive controls. Rend. Sem. Mat. Univ. Padova78 (1987) 227-235.
- F.H. Clarke, Yu.S. Ledyaev, L. Rifford and R.J. Stern, Feedback stabilization and Lyapunov functions. SIAM J. Control Optim.39 (2000) 25-48.
- F.H. Clarke, Yu.S. Ledyaev, E.D. Sontag and A.I. Subbotin, Asymptotic controllability implies feedback stabilization. IEEE Trans. Autom. Control42 (1997) 1394-1407.
- F.H. Clarke, Yu.S. Ledyaev, R.J. Stern and P.R. Wolenski, Nonsmooth Analysis and Control Theory178. Springer-Verlag, New York (1998).
- L. Rifford, Existence of Lipschitz and semi-concave control-Lyapunov functions. SIAM J. Control Optim.39 (2000) 1043-1064.
- L. Rifford, Semi-concave control-Lyapunov functions and stabilizing feedbacks. SIAM J. Control Optim.41 (2002) 659-681.
- E.D. Sontag, Stability and stabilization: discontinuities and the effect of disturbances, in Proc. NATO Advanced Study Institute – Nonlinear Analysis, Differential Equations, and Control, Montreal, Jul/Aug 1998, F.H. Clarke and R.J. Stern Eds., Kluwer (1999) 551-598.
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