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

Abstract

top
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.

How to cite

top

FEIREISL, 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
  1. 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.  Zbl0825.93636
  2. H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North Holland (1973).  Zbl0252.47055
  3. C.M. Dafermos and M. Slemrod, Asymptotic behaviour of nonlinear contraction semi-groups. J. Funct. Anal.13 (1973) 97-106.  Zbl0267.34062
  4. A. Mifdal, Stabilisation uniforme d'un système hybride, C.R. Acad. Sci. Paris, 324, Série I (1997) 37-42.  
  5. 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).  
  6. B. Rao, Decay estimates of solutions for a hybrid system of flexible structures. Eur. J. Appl. Math. (1993) 303-319.  Zbl0786.73039
  7. D.L. Russell, Decay rates for weakly damped systems in Hilbert space obtained with control-theoretic methods. J. Diff. Eq.19 (1975) 344-370.  Zbl0326.93018

NotesEmbed ?

top

You 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.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.