Geodesic
Output Stabilization for Infinite-Dimensional Bilinear Systems
International Journal of Applied Mathematics and Computer Science, Tome 15 (2005) no. 2, pp. 187-195.

Voir la notice de l'article provenant de la source Library of Science

The purpose of this paper is to extend results on regional internal stabilization for infinite bilinear systems to the case where the subregion of interest is a part of the boundary of the system evolution domain. Then we characterize either stabilizing control on a boundary part, or the one minimizing a given cost of performance. The obtained results are illustrated with numerical examples.
Keywords: infinite bilinear systems, output stabilization, regional stabilization
Mots-clés : system dwuliniowy nieskończony, stabilizacja wyjściowa, stabilizacja dziedzinowa 
@article{IJAMCS_2005_15_2_a1,
     author = {Zerrik, E. H. and Ouzahra, M.},
     title = {Output {Stabilization} for {Infinite-Dimensional} {Bilinear} {Systems}},
     journal = {International Journal of Applied Mathematics and Computer Science},
     pages = {187--195},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IJAMCS_2005_15_2_a1/}
}
TY  - JOUR
AU  - Zerrik, E. H.
AU  - Ouzahra, M.
TI  - Output Stabilization for Infinite-Dimensional Bilinear Systems
JO  - International Journal of Applied Mathematics and Computer Science
PY  - 2005
SP  - 187
EP  - 195
VL  - 15
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IJAMCS_2005_15_2_a1/
LA  - en
ID  - IJAMCS_2005_15_2_a1
ER  - 
%0 Journal Article
%A Zerrik, E. H.
%A Ouzahra, M.
%T Output Stabilization for Infinite-Dimensional Bilinear Systems
%J International Journal of Applied Mathematics and Computer Science
%D 2005
%P 187-195
%V 15
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IJAMCS_2005_15_2_a1/
%G en
%F IJAMCS_2005_15_2_a1
Zerrik, E. H.; Ouzahra, M. Output Stabilization for Infinite-Dimensional Bilinear Systems. International Journal of Applied Mathematics and Computer Science, Tome 15 (2005) no. 2, pp. 187-195. http://geodesic.mathdoc.fr/item/IJAMCS_2005_15_2_a1/

[1] Ball J. and Slemrod M. (1979): Feedback stabilization of distributed semilinear control systems.—J. Appl. Math. Opt., Vol. 5, No. 5, pp. 169–179.

[2] Ball J., Marsden J.E. and Slemrod M.(1982): Controllability for distributed bilinear systems. — SIAM. J. Contr. Optim., Vol. 20, No. 4, pp. 575–597.

[3] Chilov G. (1970): Analyse mathèmatique. Fonctions de plusieurs variables rèelles.— Moscow: Mir, (in French).

[4] Kato T. (1980): Perturbation Theory for Linear Operators. —Berlin: Springer.

[5] Pazy A. (1983): Semi-Groups of Linear Operators and Applications to Partial Differential Equations. — New York: Springer.

[6] Quinn J.P. (1980): Stabilization of bilinear systems by quadratic feedback control. — J. Math. Anal. Appl., Vol. 75, No. 1, pp. 66–80.

[7] Triggiani R. (1975): On the stabilizability problem in Banach space. —J. Math. Anal. Appl., Vol. 52, pp. 383–403.

[8] Zerrik E. and Ouzahra M. (2003a): Regional stabilization for infinite-dimensional systems. — Int. J. Contr., Vol. 76, No. 1, pp. 73–81.

[9] Zerrik E., Ouzahra M. and Ztot K. (2004): Regional stabilization for infinite bilinear systems. — IEE Contr. Theory Appl., Vol. 151, No. 1, pp. 109–116.