Asymptotic analysis and control of a hybrid system composed by two vibrating strings connected by a point mass

C. Castro

ESAIM: Control, Optimisation and Calculus of Variations (1997)

  • Volume: 2, page 231-280
  • ISSN: 1292-8119

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Castro, C.. "Asymptotic analysis and control of a hybrid system composed by two vibrating strings connected by a point mass." ESAIM: Control, Optimisation and Calculus of Variations 2 (1997): 231-280. <http://eudml.org/doc/90507>.

@article{Castro1997,
author = {Castro, C.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
language = {eng},
pages = {231-280},
publisher = {EDP Sciences},
title = {Asymptotic analysis and control of a hybrid system composed by two vibrating strings connected by a point mass},
url = {http://eudml.org/doc/90507},
volume = {2},
year = {1997},
}

TY - JOUR
AU - Castro, C.
TI - Asymptotic analysis and control of a hybrid system composed by two vibrating strings connected by a point mass
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 1997
PB - EDP Sciences
VL - 2
SP - 231
EP - 280
LA - eng
UR - http://eudml.org/doc/90507
ER -

References

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  1. [1] D. Cioranescu, P. Donato, E. Zuazua, Exact boundary controllability for the wave equation in domains with small holes, J. Math. Pures et Appl., 71, 1992, 343-377. Zbl0843.35009MR1176016
  2. [2] D. Cioranescu, P. Donato, E. Zuazua: Strong convergence on the exact controllability of the wave equation in perforated domains, in Control of Distributed Parameter Systems, Desch, Kappel and Kunisch eds., Birkhaüser-Verlag, INMS Series, 100, 1991, 99-113. Zbl0748.93009MR1155639
  3. [3] Yu. D. Galovaty, S. A. Nazarov, O. A. Oleinik, T. S. Soboleva: Eigenoscillations of a string with additional mass, Siberian Math. J., 29 (5), 1988, 744-760. Zbl0702.34050MR971229
  4. [4] S. Hansen, E. Zuazua: Exact controllability and stabilization of a vibrating string with an interior point mass, SIAM J. Cont. Optim., 33 (5), 1995, 1357-1391. Zbl0853.93018MR1348113
  5. [5] A. Haraux: Séries lacunaires et contrôle semi-interne des vibrations d'une plaque rectangulaire, J. Math. Pures et Appl., 68, 1989, 457-465. Zbl0685.93039MR1046761
  6. [6] J. L. Lions: Contrôlabilité exacte, stabilisation et perturbations de systèmes distribués. Tome 1. Contrôlabilité exacte, Masson, RMA8, 1988. Zbl0653.93002
  7. [7] J. L. Lions: Contrôlabilité exacte, stabilisation et perturbations de systèmes distribués. Tome 2, Perturbations, Masson, RMA9, 1988. Zbl0653.93003
  8. [8] A. McNabb, R. S. Anderssen, E. R. Lapwood: Asymptotic behavior of the eigenvalues of a Sturm-Liouville system with discontinuous coefficients, J. Math. Anal. Applications, 54, 1976, 741-751. Zbl0334.34031MR404752
  9. [9] O. A. Oleinick, A. S. Shamaev, B. A. Yosifian: Mathematical Problems in Elasticity and Homogenization, North-Holland, 1992. Zbl0768.73003MR1195131
  10. [10] J. Poschel, E. Trubowitz: Inverse spectral theory, Academic Press, 1986. Zbl0623.34001MR894477
  11. [11] E. Sánchez-Palencia: Nonhomogeneous Media and Vibrating Theory, Lecture Notes in Physics 127, Springer-Verlag, 1980. Zbl0432.70002MR578345
  12. [12] D. Ulrich: Divided differences and Systems of nonharmonic Fourier series, Proc. AMS, 80 (1), 1980, 47-57. Zbl0448.42009MR574507

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