Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-23T08:08:20.560Z Has data issue: false hasContentIssue false

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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