Geodesic
Strong stabilization of controlled vibrating systems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 4, pp. 1144-1157

Voir la notice de l'article provenant de la source Numdam

This paper deals with feedback stabilization of second order equations of the form ytt + A0y + u (t) B0y (t) = 0, t ∈ [0, +∞[, where A0 is a densely defined positive selfadjoint linear operator on a real Hilbert space H, with compact inverse and B0 is a linear map in diagonal form. It is proved here that the classical sufficient ad-condition of Jurdjevic-Quinn and Ball-Slemrod with the feedback control u = ⟨yt, B0y⟩H implies the strong stabilization. This result is derived from a general compactness theorem for semigroup with compact resolvent and solves several open problems.

DOI : 10.1051/cocv/2010041
Classification : 37L05, 43A60, 47D06, 47H20, 93D15
Keywords: precompactness, compact resolvent, almost periodic functions, Fourier series, mild solution, integral solution, control theory, stabilization 
@article{COCV_2011__17_4_1144_0,
     author = {Couchouron, Jean-Fran\c{c}ois},
     title = {Strong stabilization of controlled vibrating systems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1144--1157},
     publisher = {EDP-Sciences},
     volume = {17},
     number = {4},
     year = {2011},
     doi = {10.1051/cocv/2010041},
     mrnumber = {2859869},
     zbl = {1254.93082},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010041/}
}
TY  - JOUR
AU  - Couchouron, Jean-François
TI  - Strong stabilization of controlled vibrating systems
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2011
SP  - 1144
EP  - 1157
VL  - 17
IS  - 4
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010041/
DO  - 10.1051/cocv/2010041
LA  - en
ID  - COCV_2011__17_4_1144_0
ER  - 
%0 Journal Article
%A Couchouron, Jean-François
%T Strong stabilization of controlled vibrating systems
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2011
%P 1144-1157
%V 17
%N 4
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010041/
%R 10.1051/cocv/2010041
%G en
%F COCV_2011__17_4_1144_0
Couchouron, Jean-François. Strong stabilization of controlled vibrating systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 4, pp. 1144-1157. doi: 10.1051/cocv/2010041

Cité par Sources :