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).
  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. [CrossRef]
  3. J.U. Kim and Y. Renardy, Boundary control of the Timoshenko beam. SIAM J. Control Optim. 25 (1987) 1417–1429. [CrossRef] [MathSciNet]
  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]
  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.
  6. Yu.I. Lyubich and V.Q. Phóng, Asymptotic stability of linear differential equations in Banach spaces. Studia Math. 88 (1988) 34–37.
  7. R. Mennicken and M. Möller, Non-self-adjoint boundary eigenvalue problem, North-Holland Mathematics Studies 192. North-Holland, Amsterdam (2003).
  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).
  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]
  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]
  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]
  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. [CrossRef] [MathSciNet]
  13. A. Pazy, Semigroups of linear operators and applications to partial differential equations. Springer-Verlag, Berlin (1983).
  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]
  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]
  16. H. Suh and Z. Bien, Use of time-delay actions in the controller design. IEEE Trans. Automat. Contr. 25 (1980) 600–603. [CrossRef]
  17. S. Timoshenko, Vibration Problems in Engineering. Van Norstrand, New York (1955).
  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]
  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]
  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]
  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.
  22. G.Q. Xu and S.P. Yung, The expansion of semigroup and criterion of Riesz basis J. Differ. Equ. 210 (2005) 1–24.
  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]
  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]
  25. R.M. Young, An introduction to nonharmonic Fourier series. Academic Press, London (1980) 80–84.

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