Free Access
Volume 17, Number 2, April-June 2011
Page(s) 552 - 574
Published online 31 March 2010
  1. J.W. Brown and R.V. Churchill, Complex variables and applications. Seventh Edition, China Machine Press, Beijing (2004). [Google Scholar]
  2. R. Datko, Two examples of ill-posedness with respect to small time delays in stabilized elastic systems. IEEE Trans. Automat. Contr. 38 (1993) 163–166. [Google Scholar]
  3. J.U. Kim and Y. Renardy, Boundary control of the Timoshenko beam. SIAM J. Control Optim. 25 (1987) 1417–1429. [CrossRef] [MathSciNet] [Google Scholar]
  4. W.H. Kwon, G.W. Lee and S.W. Kim, Performance improvement, using time delays in multi-variable controller design. Int. J. Control 52 (1990) 1455–1473. [CrossRef] [Google Scholar]
  5. J.S. Liang, Y.Q. Chen and B.Z. Guo, A new boundary control method for beam equation with delayed boundary measurement using modified smith predictors, in Proceedings of the 42nd IEEE Conference on Decision and Control, Hawaii (2003) 809–814. [Google Scholar]
  6. Yu.I. Lyubich and V.Q. Phóng, Asymptotic stability of linear differential equations in Banach spaces. Studia Math. 88 (1988) 34–37. [Google Scholar]
  7. R. Mennicken and M. Möller, Non-self-adjoint boundary eigenvalue problem, North-Holland Mathematics Studies 192. North-Holland, Amsterdam (2003). [Google Scholar]
  8. W. Michiels and S.I. Niculescu, Stability and stabilization of time-delay systems: An Eigenvalue-based approach. Society for Industrial and Applied Mathematics, Philadelphia (2007). [Google Scholar]
  9. O. Mörgul, On the stabilization and stability robustness against small delays of some damped wave equation. IEEE Trans. Automat. Contr. 40 (1995) 1626–1630. [CrossRef] [MathSciNet] [Google Scholar]
  10. S. Nicaise and C. Pignotti, Stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks. SIAM J. Control Optim. 45 (2006) 1561–1585. [CrossRef] [MathSciNet] [Google Scholar]
  11. S. Nicaise and C. Pignotti, Stabilization of the wave equation with boundary or internal distributed delay. Differential and Integral Equations 21 (2008) 935–958. [MathSciNet] [Google Scholar]
  12. S. Nicaise and J. Valein, Stabilization of the wave equation on 1-D networks with a delay term in the nodal feedbacks. NHM 2 (2007) 425–479. [Google Scholar]
  13. A. Pazy, Semigroups of linear operators and applications to partial differential equations. Springer-Verlag, Berlin (1983). [Google Scholar]
  14. K. Sriram and M.S. Gopinathan, A two variable delay model for the circadian rhythm of Neurospora crassa. J. Theor. Biol. 231 (2004) 23–38. [CrossRef] [PubMed] [Google Scholar]
  15. J. Srividhya and M.S. Gopinathan, A simple time delay model for eukaryotic cell cycle. J. Theor. Biol. 241 (2006) 617–627. [CrossRef] [PubMed] [Google Scholar]
  16. H. Suh and Z. Bien, Use of time-delay actions in the controller design. IEEE Trans. Automat. Contr. 25 (1980) 600–603. [CrossRef] [Google Scholar]
  17. S. Timoshenko, Vibration Problems in Engineering. Van Norstrand, New York (1955). [Google Scholar]
  18. Q.P. Vu, J.M. Wang, G.Q. Xu and S.P. Yung, Spectral analysis and system of fundamental solutions for Timoshenko beams. Appl. Math. Lett. 18 (2005) 127–134. [CrossRef] [MathSciNet] [Google Scholar]
  19. G.Q. Xu and D.X. Feng, The Riesz basis property of a Timoshenko beam with boundary feedback and application. IMA J. Appl. Math. 67 (2002) 357–370. [CrossRef] [MathSciNet] [Google Scholar]
  20. G.Q. Xu and B.Z. Guo, Riesz basis property of evolution equations in Hilbert space and application to a coupled string equation. SIAM J. Control Optim. 42 (2003) 966–984. [CrossRef] [MathSciNet] [Google Scholar]
  21. G.Q. Xu and J.G. Jia, The group and Riesz basis properties of string systems with time delay and exact controllability with boundary control. IMA J. Math. Control Inf. 23 (2006) 85–96. [Google Scholar]
  22. G.Q. Xu and S.P. Yung, The expansion of semigroup and criterion of Riesz basis J. Differ. Equ. 210 (2005) 1–24. [Google Scholar]
  23. G.Q. Xu, Z.J. Han and S.P. Yung, Riesz basis property of serially connected Timoshenko beams. Int. J. Control 80 (2007) 470–485. [CrossRef] [Google Scholar]
  24. G.Q. Xu, S.P. Yung and L.K. Li, Stabilization of wave systems with input delay in the boundary control. ESAIM: COCV 12 (2006) 770–785. [CrossRef] [EDP Sciences] [Google Scholar]
  25. R.M. Young, An introduction to nonharmonic Fourier series. Academic Press, London (1980) 80–84. [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.