Volume 17, Number 2, April-June 2011
|Page(s)||552 - 574|
|Published online||31 March 2010|
- J.W. Brown and R.V. Churchill, Complex variables and applications. Seventh Edition, China Machine Press, Beijing (2004).
- 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]
- J.U. Kim and Y. Renardy, Boundary control of the Timoshenko beam. SIAM J. Control Optim. 25 (1987) 1417–1429. [CrossRef] [MathSciNet]
- 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]
- 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.
- Yu.I. Lyubich and V.Q. Phóng, Asymptotic stability of linear differential equations in Banach spaces. Studia Math. 88 (1988) 34–37.
- R. Mennicken and M. Möller, Non-self-adjoint boundary eigenvalue problem, North-Holland Mathematics Studies 192. North-Holland, Amsterdam (2003).
- 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).
- 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]
- 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]
- 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]
- 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]
- A. Pazy, Semigroups of linear operators and applications to partial differential equations. Springer-Verlag, Berlin (1983).
- 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]
- J. Srividhya and M.S. Gopinathan, A simple time delay model for eukaryotic cell cycle. J. Theor. Biol. 241 (2006) 617–627. [CrossRef] [PubMed]
- H. Suh and Z. Bien, Use of time-delay actions in the controller design. IEEE Trans. Automat. Contr. 25 (1980) 600–603. [CrossRef]
- S. Timoshenko, Vibration Problems in Engineering. Van Norstrand, New York (1955).
- 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]
- 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]
- 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]
- 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.
- G.Q. Xu and S.P. Yung, The expansion of semigroup and criterion of Riesz basis J. Differ. Equ. 210 (2005) 1–24.
- 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]
- 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]
- R.M. Young, An introduction to nonharmonic Fourier series. Academic Press, London (1980) 80–84.
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