Free Access
Volume 14, Number 3, July-September 2008
Page(s) 632 - 656
Published online 18 January 2008
  1. 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] [Google Scholar]
  2. K. Ammari, Z. Liu and M. Tucsnak, Decay rates for a beam with pointwise force and moment feedback. Math. Control Signals Systems 15 (2002) 229–255. [Google Scholar]
  3. S.A. Avdonin and S.A. Ivanov, Families of Exponentials: The Method of Moments in Controllability Problems for Distributed Parameter Systems. Cambridge University Press, Cambridge, UK (1995). [Google Scholar]
  4. S.A. Avdonin and S.A. Ivanov, Riesz bases of exponentials and divided differences. St. Petersburg Math. J. 13 (2002) 339–351. [MathSciNet] [Google Scholar]
  5. S.A. Avdonin and W. Moran, Simultaneous control problems for systems of elastic strings and beams. Syst. Control Lett. 44 (2001) 147–155. [Google Scholar]
  6. C. Castro and E. Zuazua, A hybrid system consisting of two flexible beams connected by a point mass: spectral analysis and well-posedness in asymmetric spaces. ESAIM: Proc. 2 (1997) 17–53. [Google Scholar]
  7. C. Castro and E. Zuazua, Boundary controllability of a hybrid system consisting in two flexible beams connected by a point mass. SIAM J. Control Optim. 36 (1998) 1576–1595. [Google Scholar]
  8. C. Castro and E. Zuazua, Exact boundary controllability of two Euler-Bernoulli beams connected by a point mass. Math. Comput. Modelling 32 (2000) 955–969. [CrossRef] [MathSciNet] [Google Scholar]
  9. G. Chen, M.C. Delfour, A.M. Krall and G. Payre, Modeling, stabilization and control of serially connected beams. SIAM J. Control Optim. 25 (1987) 526–546. [CrossRef] [MathSciNet] [Google Scholar]
  10. G. Chen, S.G. Krantz, D.L. Russell, C.E. Wayne, H.H. West and M.P. Coleman, Analysis, designs, and behavior of dissipative joints for coupled beams. SIAM J. Appl. Math. 49 (1989) 1665–1693. [CrossRef] [MathSciNet] [Google Scholar]
  11. S. Cox and E. Zuazua, The rate at which energy decays in a damped string. Comm. Partial Diff. Eq. 19 (1994) 213–243. [Google Scholar]
  12. S. Cox and E. Zuazua, The rate at which energy decays in a string damped at one end. Indiana Univ. Math. J. 44 (1995) 545–573. [MathSciNet] [Google Scholar]
  13. R.F. Curtain and G. Weiss, Exponential stabilization of well-posed systems by colocated feedback. SIAM J. Control Optim. 45 (2006) 273–297. [Google Scholar]
  14. R. Dáger and E. Zuazua, Wave Propagation, Observation and Control in 1-d Flexible Multi-Structures, Mathématiques et Applications 50. Springer-Verlag, Berlin (2006). [Google Scholar]
  15. B.Z. Guo and K.Y. Chan, Riesz basis generation, eigenvalues distribution, and exponential stability for a Euler-Bernoulli beam with joint feedback control. Rev. Mat. Complut. 14 (2001) 205–229. [MathSciNet] [Google Scholar]
  16. B.Z. Guo and J.M. Wang, Riesz basis generation of an abstract second-order partial differential equation system with general non-separated boundary conditions. Numer. Funct. Anal. Optim. 27 (2006) 291–328. [CrossRef] [MathSciNet] [Google Scholar]
  17. B.Z. Guo and G.Q. Xu, Riesz basis and exact controllability of C0-groups with one-dimensional input operators. Syst. Control Lett. 52 (2004) 221–232. [Google Scholar]
  18. B.Z. Guo and G.Q. Xu, Expansion of solution in terms of generalized eigenfunctions for a hyperbolic system with static boundary condition. J. Funct. Anal. 231 (2006) 245–268. [CrossRef] [MathSciNet] [Google Scholar]
  19. B.Ya. Levin, On bases of exponential functions in L2. Zapiski Math. Otd. Phys. Math. Facul. Khark. Univ. 27 (1961) 39–48 (in Russian). [Google Scholar]
  20. K.S. Liu and Z. Liu, Exponential decay of energy of vibrating strings with local viscoelasticity. Z. Angew. Math. Phys. 53 (2002) 265–280. [CrossRef] [MathSciNet] [Google Scholar]
  21. K.S. Liu and B. Rao, Exponential stability for the wave equations with local Kelvin-Voigt damping. Z. Angew. Math. Phys. 57 (2006) 419–432. [CrossRef] [MathSciNet] [Google Scholar]
  22. Z.H. Luo, B.Z. Guo and Ö. Morgül, Stability and Stabilization of Linear Infinite Dimensional Systems with Applications. Springer-Verlag, London (1999). [Google Scholar]
  23. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, New York (1983). [Google Scholar]
  24. R. Rebarber, Exponential stability of coupled beams with dissipative joints: a frequency domain approach. SIAM J. Control Optim. 33 (1995) 1–28. [Google Scholar]
  25. M. Renardy, On the linear stability of hyperbolic PDEs and viscoelastic flows. Z. Angew. Math. Phys. 45 (1994) 854–865. [CrossRef] [MathSciNet] [Google Scholar]
  26. A.A. Shkalikov, Boundary problems for ordinary differential equations with parameter in the boundary conditions. J. Soviet Math. 33 (1986) 1311–1342. [CrossRef] [Google Scholar]
  27. J.M. Wang and S.P. Yung, Stability of a nonuniform Rayleigh beam with internal dampings. Syst. Control Lett. 55 (2006) 863–870. [Google Scholar]
  28. G. Weiss and R.F. Curtain, Exponential stabilization of a Rayleigh beam using colocated control. IEEE Trans. Automatic Control (to appear). [Google Scholar]
  29. G.Q. Xu and B.Z. Guo, Riesz basis property of evolution equations in Hilbert spaces and application to a coupled string equation. SIAM J. Control Optim. 42 (2003) 966–984. [CrossRef] [MathSciNet] [Google Scholar]
  30. G.Q. Xu and S.P. Yung, Stabilization of Timoshenko beam by means of pointwise controls. ESAIM: COCV 9 (2003) 579–600. [CrossRef] [EDP Sciences] [Google Scholar]
  31. R.M. Young, An Introduction to Nonharmonic Fourier Series. Academic Press, Inc., London (1980). [Google Scholar]

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