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.
@article{bwmeta1.element.bwnjournal-article-amcv15i2p187bwm, author = {Zerrik, El and Ouzahra, Mohamed}, title = {Output stabilization for infinite-dimensional bilinear systems}, journal = {International Journal of Applied Mathematics and Computer Science}, volume = {15}, year = {2005}, pages = {187-195}, zbl = {1086.93053}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv15i2p187bwm} }
Zerrik, El; Ouzahra, Mohamed. Output stabilization for infinite-dimensional bilinear systems. International Journal of Applied Mathematics and Computer Science, Tome 15 (2005) pp. 187-195. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv15i2p187bwm/
[000] Ball J. and Slemrod M. (1979): Feedback stabilization of distributed semilinear control systems. - J. Appl. Math. Opt., Vol. 5, No. 5, pp. 169-179. | Zbl 0405.93030
[001] 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. | Zbl 0485.93015
[002] Chilov G. (1970): Analyse mathèmatique. Fonctions de plusieurs variables rèelles. - Moscow: Mir, (in French). | Zbl 0317.26011
[003] Kato T. (1980): Perturbation Theory for Linear Operators. - Berlin: Springer. | Zbl 0435.47001
[004] Pazy A. (1983): Semi-Groups of Linear Operators and Applications to Partial Differential Equations. - New York: Springer. | Zbl 0516.47023
[005] Quinn J.P. (1980): Stabilization of bilinear systems by quadratic feedback control.- J. Math. Anal. Appl., Vol. 75, No. 1, pp. 66-80. | Zbl 0438.93054
[006] Triggiani R. (1975): On the stabilizability problem in Banach space. - J. Math. Anal. Appl., Vol. 52, pp. 383-403. | Zbl 0326.93023
[007] Zerrik E. and Ouzahra M. (2003a): Regional stabilization for infinite-dimensional systems.- Int. J. Contr., Vol. 76, No. 1, pp. 73-81. | Zbl 1037.93070
[008] 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.