Stabilization of a hybrid system with a nonlinear nonmonotone feedback
Eduard FEIREISL; Geoffrey O'DOWD
ESAIM: Control, Optimisation and Calculus of Variations (2010)
- Volume: 4, page 123-135
- ISSN: 1292-8119
Access Full Article
top
Abstract
topHow to cite
topFEIREISL, Eduard, and O'DOWD, Geoffrey. "Stabilization of a hybrid system with a nonlinear nonmonotone feedback." ESAIM: Control, Optimisation and Calculus of Variations 4 (2010): 123-135. <http://eudml.org/doc/116569>.
@article{FEIREISL2010,
abstract = {
For a hybrid system composed of a cable with masses at both ends,
we prove the existence of solutions for a class of nonlinear and
nonmonotone feedback laws by means of a priori estimates. Assuming
some local monotonicity, strong stabilization
is obtained thanks to some Riemann's invariants technique and La
Salle's principle.
},
author = {FEIREISL, Eduard, O'DOWD, Geoffrey},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Hybrid systems; wave equation; stabilization by
feedback law; Riemann invariants; well-posedness; hybrid system; evolution equation; maximal monotone operators; stabilization; local monotonicity; La Salle's principle},
language = {eng},
month = {3},
pages = {123-135},
publisher = {EDP Sciences},
title = {Stabilization of a hybrid system with a nonlinear nonmonotone feedback},
url = {http://eudml.org/doc/116569},
volume = {4},
year = {2010},
}
TY - JOUR
AU - FEIREISL, Eduard
AU - O'DOWD, Geoffrey
TI - Stabilization of a hybrid system with a nonlinear nonmonotone feedback
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 4
SP - 123
EP - 135
AB -
For a hybrid system composed of a cable with masses at both ends,
we prove the existence of solutions for a class of nonlinear and
nonmonotone feedback laws by means of a priori estimates. Assuming
some local monotonicity, strong stabilization
is obtained thanks to some Riemann's invariants technique and La
Salle's principle.
LA - eng
KW - Hybrid systems; wave equation; stabilization by
feedback law; Riemann invariants; well-posedness; hybrid system; evolution equation; maximal monotone operators; stabilization; local monotonicity; La Salle's principle
UR - http://eudml.org/doc/116569
ER -
References
top- B. D'Andréa-Novel, F. Boustany, F. Conrad and B. Rao, Feedback stabilization of a hybrid PDE-ODE system. Math. Control Signals Systems (1994) 1-22.
- H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North Holland (1973).
- C.M. Dafermos and M. Slemrod, Asymptotic behaviour of nonlinear contraction semi-groups. J. Funct. Anal.13 (1973) 97-106.
- A. Mifdal, Stabilisation uniforme d'un système hybride, C.R. Acad. Sci. Paris, 324, Série I (1997) 37-42.
- A. Mifdal, Étude de la stabilité forte et uniforme d'un système hybride. Application à un modèle de pont roulant, Thèse de l'Université de Nancy I (1997).
- B. Rao, Decay estimates of solutions for a hybrid system of flexible structures. Eur. J. Appl. Math. (1993) 303-319.
- D.L. Russell, Decay rates for weakly damped systems in Hilbert space obtained with control-theoretic methods. J. Diff. Eq.19 (1975) 344-370.
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.