Free access
Issue
ESAIM: COCV
Volume 9, March 2003
Page(s) 579 - 600
DOI http://dx.doi.org/10.1051/cocv:2003028
Published online 15 September 2003
  1. G. Chen, C.M. Delfour, A.M. Krall and G. Payre, Modeling, stabilization and control of serially connected beam. SIAM J. Control Optim. 25 (1987) 526-546. [CrossRef] [MathSciNet]
  2. G. Chen, S.G. Krantz, D.W. Ma, C.E. Wayne and H.H. West, The Euler-Bernoulli beam equation with boundary energy dissipation, in Operator methods for optimal control problems, edited by Sung J. Lee. Marcel Dekker, New York (1988) 67-96.
  3. G. Chen, S.G. Krantz, D.L. Russell, C.E. Wayne and H.H. West, Analysis, design and behavior of dissipative joints for coupled beams. SIAM J. Appl. Math. 49 (1989) 1665-1693. [CrossRef] [MathSciNet]
  4. F. Conrad, Stabilization of beams by pointwise feedback control. SIAM J. Control Optim. 28 (1990) 423-437. [CrossRef] [MathSciNet]
  5. J.E. Lagnese, G. Leugering and E. Schmidt, Modeling, analysis and control of dynamic Elastic Multi-link structures. Birkhauser, Basel (1994).
  6. R. Rebarber, Exponential stability of coupled beam with dissipative joints: A frequency domain approach. SIAM J. Control Optim. 33 (1995) 1-28. [CrossRef] [MathSciNet]
  7. K. Ammari and M. Tucsnak, Stabilization of Bernoulli-Euler beams by means of a pointwise feedback force. SIAM J. Control Optim. 39 (2000) 1160-1181. [CrossRef] [MathSciNet]
  8. J.U. Kim and Y. Renardy, Boundary control of the Timoshenko beam. SIAM. J. Control Optim. 25 (1987) 1417-1429. [CrossRef] [MathSciNet]
  9. K. Ito and N. Kunimatsu, Semigroup model and stability of the structurally damped Timoshenko beam with boundary inputs. Int. J. Control 54 (1991) 367-391. [CrossRef]
  10. Ö. Morgül, Boundary control of a Timoshenko beam attached to a rigid body: Planar motion. Int. J. Control 54 (1991) 763-791. [CrossRef]
  11. D.H. Shi and D.X. Feng, Feedback stabilization of a Timoshenko beam with an end mass. Int. J. Control 69 (1998) 285-300. [CrossRef]
  12. D.X. Feng, D.H. Shi and W.T. Zhang, Boundary feedback stabilization of Timoshenko beam with boundary dissipation. Sci. China Ser. A 41 (1998) 483-490. [CrossRef] [MathSciNet]
  13. F. Conrad and Ö. Morgül, On the stabilization of a flexible beam with a tip mass. SIAM J. Control Optim. 36 (1998) 1962-1986. [CrossRef] [MathSciNet]
  14. B.Z. Guo and R.Y. Yu, The Riesz basis property of discrete operators and application to a Euler-Bernoulli beam equation with boundary linear feedback control. IMA J. Math. Control Inform. 18 (2001) 241-251. [CrossRef] [MathSciNet]
  15. B.P. Rao, Optimal energy decay rate in a damped Rayleigh beam, edited by S. Cox and I. Lasiecka. Contemp. Math. 209 (1997) 221-229.
  16. G.Q. Xu, Boundary feedback control of elastic beams, Ph.D. Thesis. Institute of Mathematics and System Science, Chinese Academy of Sciences (2000).
  17. A. Pazy, Semigroups of linear operators and applications to partial differential equations. Springer-Verlag, New York, Appl. Math. Sci. 44 (1983).
  18. R.M. Young An introduction to nonharmonic Fourier series. Academic Press, Inc. New York (1980).