Nonlinear feedback stabilization of a rotating body-beam without damping
Boumediène Chentouf; Jean-François Couchouron
ESAIM: Control, Optimisation and Calculus of Variations (1999)
- Volume: 4, page 515-535
- ISSN: 1292-8119
Access Full Article
topHow to cite
topChentouf, Boumediène, and Couchouron, Jean-François. "Nonlinear feedback stabilization of a rotating body-beam without damping." ESAIM: Control, Optimisation and Calculus of Variations 4 (1999): 515-535. <http://eudml.org/doc/90552>.
@article{Chentouf1999,
author = {Chentouf, Boumediène, Couchouron, Jean-François},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {nonlinear control; exponential stability; exponential decay of the beam vibrations},
language = {eng},
pages = {515-535},
publisher = {EDP Sciences},
title = {Nonlinear feedback stabilization of a rotating body-beam without damping},
url = {http://eudml.org/doc/90552},
volume = {4},
year = {1999},
}
TY - JOUR
AU - Chentouf, Boumediène
AU - Couchouron, Jean-François
TI - Nonlinear feedback stabilization of a rotating body-beam without damping
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 1999
PB - EDP Sciences
VL - 4
SP - 515
EP - 535
LA - eng
KW - nonlinear control; exponential stability; exponential decay of the beam vibrations
UR - http://eudml.org/doc/90552
ER -
References
top- [1] J. Ackermann, Sampled-data control system: Analysis and synthesis, robust system design, Springer-Verlag ( 1985). Zbl0639.93001MR699111
- [2] J. Baillieul and M. Levi, Rotational elastic dynamics. Physica D, 27 ( 1987) 43-62. Zbl0644.73054MR912850
- [3] P. Bénilan, Équations d'évolution dans un espace de Banach quelconque et applications, Thèse, Paris XI, Orsay ( 1972). Zbl0246.47068
- [4] P. Bénilan, M.G. Crandal and A. Pazy, Nonlinear evolution equations in Banach spaces, monograph in preparation.
- [5] A.M. Bloch and E.S. Titi, On the dynamics of rotating elastic beams, in Proc. Conf. New Trends Syst. theory, Genoa, Italy, July 9-11, 1990, Conte, Perdon, and Wyman, eds., Cambridge, MA: Birkhäuser ( 1990). Zbl0759.73036MR1125101
- [6] H. Brezis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hubert, North-Holland, Amsterdam, London ( 1973). Zbl0252.47055MR348562
- [7] H. Brezis, Analyse Fonctionnelle. Théorie et applications, Masson ( 1983). Zbl0511.46001MR697382
- [8] F. Conrad and B. Rao, Decay of solutions of the wave equation in a star-shaped domain with nonlinear boundary feedback. Asymptotic Analysis, 7 ( 1993) 159-177. Zbl0791.35011MR1226972
- [9] J.-M. Coron and B. d'Andréa-Novel, Stabilization of a rotating body-beam without damping. IEEE Trans. Automat. Contr., 43 ( 1998) 608-618. Zbl0908.93055MR1618052
- [10] M.G. Crandall, Nonlinear semigroups and evolution governed by accretive operators. Pro. Sympo. in pure Math. 45 ( 1986) 305-337. Zbl0637.47039MR843569
- [11] C.M. Dafermos and M. Slemrod, Asymptotic behaviour of non linear contractions semi-groups, J. Func. Anal. 14 ( 1973) 97-106. Zbl0267.34062MR346611
- [12] A. Haraux, Systems Dynamique Dissipatifs et Applications. Collection RMA (17) Masson, Paris ( 1991). Zbl0726.58001MR1084372
- [13] V. Jurdjevic and J. P. Quin, Controllability and stability, J. Differential Equations, 28 ( 1978) 381-389. Zbl0417.93012
- [14] V. Komornik and E. Zuazua, A direct method for the boundary stabilization of the wave equation. J. Math. Pures Appl., 69 ( 1990) 33-54. Zbl0636.93064
- [15] V. Komornik, Exact Controllability and Stabilization. The Multiplier Method, Masson and John Wiley ( 1994). Zbl0937.93003
- [16] H. Laousy, C.Z. Xu and G. Sallet, Boundary feedback stabilization of a rotating body-beam system. IEEE Trans. Automat. Contr., 41 ( 1996) 241-245. Zbl0847.93026
- [17] O. Morgül, Orientation and stabilization of a flexible beam attached to a rigid body: Planar motion, IEEE Trans. Automat. Contr., 36 ( 1991) 953-963. Zbl0731.73054
- [18] O. Morgül, Constant angular velocity control of a rotating flexible structure, in Proc. 2nd Conf., ECC'93., Groningen, Netherlands ( 1993) 299-302.
- [19] O. Morgül, Control of a rotating flexible structure. IEEE Trans. Automat. Contr. 39 ( 1994) 351-356. Zbl0800.93590MR1261712
- [20] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer Verlag, New York ( 1983). Zbl0516.47023MR710486
- [21] M. Pierre, Perturbations localement lipschitziennes et continues d'opérateurs m-accretifs. Proc. Amer. Math. Soc., 58 ( 1976) 124-128. Zbl0308.47047MR417863
- [22] B. Rao, Decay estimate of solution for hybrid system of flexible structures. Euro. J. Appl. Math. 4 ( 1993) 303-319. Zbl0786.73039MR1236344
- [23] C.Z. Xu and J. Baillieul, Stabilizability and stabilization of a rotating body-beam system with torque control. IEEE Trans. Automat. Contr. 38 ( 1993) 1754-1765. Zbl0825.93675MR1254313
- [24] C.Z. Xu and G. Sallet, Boundary stabilization of a rotating flexible system. Lecture Notes in Control and Information Sciences 185, R.F. Curtain, A. Bensoussan and J.L. Lions, eds., Springer Verlag, New York ( 1992) 347-365. Zbl0792.93069MR1208280
- [25] A. Zeidler, Non linear functional analysis and its applications, Vol. 2, Springer Verlag, New York ( 1986). Zbl0583.47050
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.