EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 14 / No 3 (July-September 2008) ESAIM: COCV, 14 3 (2008) 632-656 References
Free Access
Issue
ESAIM: COCV
Volume 14, Number 3, July-September 2008
Page(s) 632 - 656
DOI https://doi.org/10.1051/cocv:2008001
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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.