Singular perturbations for systems of differential inclusions

Marc Quincampoix

Banach Center Publications (1995)

  • Volume: 32, Issue: 1, page 341-348
  • ISSN: 0137-6934

Abstract

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We study a system of two differential inclusions such that there is a singular perturbation in the second one. We state new convergence results of solutions under assumptions concerning contingent derivative of the perturbed inclusion. These results state that there exists at least one family of solutions which converges to some solution of the reduced system. We extend this result to perturbed systems with state constraints.

How to cite

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Quincampoix, Marc. "Singular perturbations for systems of differential inclusions." Banach Center Publications 32.1 (1995): 341-348. <http://eudml.org/doc/262848>.

@article{Quincampoix1995,
abstract = {We study a system of two differential inclusions such that there is a singular perturbation in the second one. We state new convergence results of solutions under assumptions concerning contingent derivative of the perturbed inclusion. These results state that there exists at least one family of solutions which converges to some solution of the reduced system. We extend this result to perturbed systems with state constraints.},
author = {Quincampoix, Marc},
journal = {Banach Center Publications},
keywords = {system of two differential inclusions; singular perturbation; convergence; contingent derivative; perturbed inclusion},
language = {eng},
number = {1},
pages = {341-348},
title = {Singular perturbations for systems of differential inclusions},
url = {http://eudml.org/doc/262848},
volume = {32},
year = {1995},
}

TY - JOUR
AU - Quincampoix, Marc
TI - Singular perturbations for systems of differential inclusions
JO - Banach Center Publications
PY - 1995
VL - 32
IS - 1
SP - 341
EP - 348
AB - We study a system of two differential inclusions such that there is a singular perturbation in the second one. We state new convergence results of solutions under assumptions concerning contingent derivative of the perturbed inclusion. These results state that there exists at least one family of solutions which converges to some solution of the reduced system. We extend this result to perturbed systems with state constraints.
LA - eng
KW - system of two differential inclusions; singular perturbation; convergence; contingent derivative; perturbed inclusion
UR - http://eudml.org/doc/262848
ER -

References

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  10. [10] H. Frankowska, S. Plaskacz and T. Rzeżuchowski, Measurable viability theorems and Hamilton-Jacobi-Bellman equation, J. Differential Equations 116 (1995), 265-305. Zbl0836.34016
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  14. [14] H. Tuan, Asymptotical solution of differential systems with multivalued right-hand side, Ph.D. Thesis, University of Odessa, 1990, in Russian. 
  15. [15] M. Quincampoix, Contribution à l'étude des perturbations singulières pour les systèmes contrôlés et les inclusions différentielles, C. R. Acad. Sci. Paris Sér. I 316 (1993), 133-138. Zbl0769.93055
  16. [16] M. Quincampoix, Singular perturbations for control systems and for differential inclusions, in: Cahiers Mathématiques de la Décision, Université Paris-Dauphine, 1994. 
  17. [17] V. M. Veliov, Differential inclusions with stable subinclusions, Nonlinear Anal. 23 (1994), 1027-1038. Zbl0816.34011

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