Output stabilization for infinite-dimensional bilinear systems

El Zerrik; Mohamed Ouzahra

International Journal of Applied Mathematics and Computer Science (2005)

  • Volume: 15, Issue: 2, page 187-195
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Zerrik, El, and Ouzahra, Mohamed. "Output stabilization for infinite-dimensional bilinear systems." International Journal of Applied Mathematics and Computer Science 15.2 (2005): 187-195. <http://eudml.org/doc/207734>.

@article{Zerrik2005,
abstract = {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.},
author = {Zerrik, El, Ouzahra, Mohamed},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {infinite bilinear systems; output stabilization; regionalstabilization; regional stabilization},
language = {eng},
number = {2},
pages = {187-195},
title = {Output stabilization for infinite-dimensional bilinear systems},
url = {http://eudml.org/doc/207734},
volume = {15},
year = {2005},
}

TY - JOUR
AU - Zerrik, El
AU - Ouzahra, Mohamed
TI - Output stabilization for infinite-dimensional bilinear systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2005
VL - 15
IS - 2
SP - 187
EP - 195
AB - 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.
LA - eng
KW - infinite bilinear systems; output stabilization; regionalstabilization; regional stabilization
UR - http://eudml.org/doc/207734
ER -

References

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  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. Zbl0405.93030
  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. Zbl0485.93015
  3. Chilov G. (1970): Analyse mathèmatique. Fonctions de plusieurs variables rèelles. - Moscow: Mir, (in French). Zbl0317.26011
  4. Kato T. (1980): Perturbation Theory for Linear Operators. - Berlin: Springer. Zbl0435.47001
  5. Pazy A. (1983): Semi-Groups of Linear Operators and Applications to Partial Differential Equations. - New York: Springer. Zbl0516.47023
  6. Quinn J.P. (1980): Stabilization of bilinear systems by quadratic feedback control.- J. Math. Anal. Appl., Vol. 75, No. 1, pp. 66-80. Zbl0438.93054
  7. Triggiani R. (1975): On the stabilizability problem in Banach space. - J. Math. Anal. Appl., Vol. 52, pp. 383-403. Zbl0326.93023
  8. Zerrik E. and Ouzahra M. (2003a): Regional stabilization for infinite-dimensional systems.- Int. J. Contr., Vol. 76, No. 1, pp. 73-81. Zbl1037.93070
  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. 

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