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Decay estimates of solutions for a hybrid system of flexible structures

Published online by Cambridge University Press:  26 September 2008

Bopeng Rao
Affiliation:
Université de Nancy I, U. R. A. CNRS 750, Laboratoire de Mathématiques and Projet Numath, INRIA Lorraine, B.P.239, 54506 Vandœuvre-lès-Nancy, France

Abstract

We consider a hybrid system consisting of a cable linked at its end to a rigid body. It is proved that such a hybrid system can be asymptotically stabilized by means of dissipative boundary feedbacks. Uniform decay estimates of energy are also established.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1993

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References

[1]Littman, W. & Markus, L. 1988 Stabilization of a hybrid system of elasticity by feedback boundary damping. Annali di Matematica Pura ed Applicata 152, 281330.CrossRefGoogle Scholar
[2]Littman, W. & Markus, L. 1987 Some recent results on control and stabilization of flexible structures. In: Proc. COMCON Workshop, Montpellier, France, December.Google Scholar
[3]Slemrod, M. 1989 Feedback stabilization of a linear system in Hilbert space with an a priori bounded control. Math. Control Signals Systems 2, 265285.Google Scholar
[4]Lions, J. L. & Magenes, E. 1968 Problémes aux Limites non Homogénes, Vol. I. Dunod.Google Scholar
[5]Brezis, H. 1973 Opèrateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert. North-Holland.Google Scholar
[6]Haraux, A. 1987 Semilinear hyperbolic problems in bounded domain. In: Dieudonné, J., editor, Math. Report, Vol. 3. Harwood Academic Publishers, Gordon and Breach.Google Scholar
[7]Dafermos, C. M. & Slemrod, M. 1973 Asymptotic behavior of nonlinear contraction semigroups. J. Func. Anal. 13, 97106.Google Scholar
[8]Conrad, F. & Rao, B. P. 1991 Decay of solutions of wave equation in a star-shaped domain with nonlinear boundary feedback. Rapport de Recherche de 1'INRIA No. 1381, Rocquencourt, France.Google Scholar
[9]Rao, B. P. 1992 Stabilization of Kirchhoff plate equation in star-shaped domain by nonlinear boundary feedback. J. Nonlinear Analysis.CrossRefGoogle Scholar
[10]déAndrea-Novel, B., Boustany, F. & Rao, B. P. 1991 Control of an overhead crane: feedback stabilization of a hybrid PDE-ODE system. In: Proc. European Control Conf., Grenoble, July.Google Scholar
[11]Lee, E. B. & You, Y. C. 1987 Stabilization of a hybrid (string/point mass) system. In: Proc. 5th Int. Conf. on System Engineering,Dayton, OH,September.Google Scholar