FEEDBACK STABILIZATION OF A COUPLED STRING-BEAM SYSTEM

被引:21
作者
Ammari, Kais [1 ]
Jellouli, Mohamed [1 ]
Mehrenberger, Michel [2 ]
机构
[1] Fac Sci Monastir, Dept Math, Monastir 5019, Tunisia
[2] Univ Strasbourg, Inst Rech Math Avancee, F-67084 Strasbourg, France
关键词
Observability; Feedback stabilization; Coupled string-beam system;
D O I
10.3934/nhm.2009.4.19
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We consider a stabilization problem for a coupled string-beam system. We prove some decay results of the energy of the system. The method used is based on the methodology introduced in Ammari and Tucsnak [2] where the exponential and weak stability for the closed loop problem is reduced to a boundedness property of the transfer function of the associated open loop system. Morever, we prove, for the same model but with two control functions, independently of the length of the beam that the energy decay with a polynomial rate for all regular initial data. The method used, in this case, is based on a frequency domain method and combine a contradiction argument with the multiplier technique to carry out a special analysis for the resolvent.
引用
收藏
页码:19 / 34
页数:16
相关论文
共 13 条
  • [1] Stabilization of Bernoulli-Euler beams by means of a pointwise feedback force
    Ammari, K
    Tucsnak, M
    [J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2000, 39 (04) : 1160 - 1181
  • [2] Stabilization of second order evolution equations by a class of unbounded feedbacks
    Ammari, K
    Tucsnak, M
    [J]. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2001, 6 (14): : 361 - 386
  • [3] AMMARI K, NODAL FEEDBACK UNPUB
  • [4] Stabilization of generic trees of strings
    Ammart, K
    Jellouli, M
    Khenissi, M
    [J]. JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2005, 11 (02) : 177 - 193
  • [5] [Anonymous], 1996, Smart Material Structures: Modeling, Estimation and Control
  • [6] NON-HARMONIC FOURIER-SERIES AND THE STABILIZATION OF DISTRIBUTED SEMI-LINEAR CONTROL-SYSTEMS
    BALL, JM
    SLEMROD, M
    [J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1979, 32 (04) : 555 - 586
  • [7] Brezis H., 1999, Analyse fonctionnelle, theorie et applications
  • [8] Cassels JW, 1966, INTRO DIOPHANTINE AP
  • [9] Lagnese J., 1994, MODELING ANAL DYNAMI
  • [10] LANG S., 1966, Introduction to Diophantine Approximations