Geodesic
An optimisation approach for stability analysis and controller synthesis of linear hyperbolic systems
Lamare, Pierre-Olivier1  ; Girard, Antoine2  ; Prieur, Christophe3 
1 BIOCORE project-team, Inria Sophia Antipolis – Méditerranée, 2004 route des Lucioles, BP 93, 06902 Sophia Antipolis cedex, France.
2 Laboratoire des signaux et systèmes (L2S), CNRS, Centrale Supélec, Université Paris-Sud, Université Paris-Saclay, 3, rue Joliot-Curie, 91192 Gif-sur-Yvette cedex, France.
3 Department of Automatic Control, Gipsa-lab, 11 rue des Mathématiques, BP 46, 38402 Saint Martin d’Hères cedex, France.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 1236-1263

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

In this paper, we consider the problems of stability analysis and control synthesis for first-order hyperbolic linear Partial Differential Equations (PDEs) over a bounded interval with spatially varying coefficients. We propose Linear Matrix Inequalities (LMI) conditions for the stability and for the design of boundary and distributed control for the system. These conditions involve an infinite number of LMI to solve. Hence, we show how to overapproximate these constraints using polytopic embeddings to reduce the problem to a finite number of LMI. We show the effectiveness of the overapproximation with several examples and with the Saint-Venant equations with friction.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2016038
Classification : 49J20, 37N35, 93B52
Keywords: Hyperbolic PDE, Lyapunov method, LMI

Lamare, Pierre-Olivier 1 ; Girard, Antoine 2 ; Prieur, Christophe 3

1 BIOCORE project-team, Inria Sophia Antipolis – Méditerranée, 2004 route des Lucioles, BP 93, 06902 Sophia Antipolis cedex, France.
2 Laboratoire des signaux et systèmes (L2S), CNRS, Centrale Supélec, Université Paris-Sud, Université Paris-Saclay, 3, rue Joliot-Curie, 91192 Gif-sur-Yvette cedex, France.
3 Department of Automatic Control, Gipsa-lab, 11 rue des Mathématiques, BP 46, 38402 Saint Martin d’Hères cedex, France. 
@article{COCV_2016__22_4_1236_0,
     author = {Lamare, Pierre-Olivier and Girard, Antoine and Prieur, Christophe},
     title = {An optimisation approach for stability analysis and controller synthesis of linear hyperbolic systems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1236--1263},
     publisher = {EDP-Sciences},
     volume = {22},
     number = {4},
     year = {2016},
     doi = {10.1051/cocv/2016038},
     zbl = {1353.49036},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2016038/}
}
TY  - JOUR
AU  - Lamare, Pierre-Olivier
AU  - Girard, Antoine
AU  - Prieur, Christophe
TI  - An optimisation approach for stability analysis and controller synthesis of linear hyperbolic systems
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2016
SP  - 1236
EP  - 1263
VL  - 22
IS  - 4
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2016038/
DO  - 10.1051/cocv/2016038
LA  - en
ID  - COCV_2016__22_4_1236_0
ER  - 
%0 Journal Article
%A Lamare, Pierre-Olivier
%A Girard, Antoine
%A Prieur, Christophe
%T An optimisation approach for stability analysis and controller synthesis of linear hyperbolic systems
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2016
%P 1236-1263
%V 22
%N 4
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2016038/
%R 10.1051/cocv/2016038
%G en
%F COCV_2016__22_4_1236_0
Lamare, Pierre-Olivier; Girard, Antoine; Prieur, Christophe. An optimisation approach for stability analysis and controller synthesis of linear hyperbolic systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 1236-1263. doi: 10.1051/cocv/2016038

Cité par Sources :