Free Access
Issue |
ESAIM: COCV
Volume 16, Number 2, April-June 2010
|
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Page(s) | 420 - 456 | |
DOI | https://doi.org/10.1051/cocv/2009007 | |
Published online | 21 April 2009 |
- C. Abdallah, P. Dorato, J. Benitez-Read and R. Byrne, Delayed positive feedback can stabilize oscillatory systems, in ACC' 93 (American Control Conference), San Francisco (1993) 3106–3107. [Google Scholar]
- 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 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
- K. Ammari and M. Tucsnak, Stabilization of second order evolution equations by a class of unbounded feedbacks. ESAIM: COCV 6 (2001) 361–386 (electronic). [CrossRef] [EDP Sciences] [Google Scholar]
- K. Ammari, E.M. Ait Ben Hassi, S. Boulite and L. Maniar, Feedback stabilization of a class of evolution equations with delay. J. Evol. Eq. (Submitted). [Google Scholar]
- W. Arendt and C.J.K. Batty, Tauberian theorems and stability of one-parameter semigroups. Trans. Amer. Math. Soc. 305 (1988) 837–852. [Google Scholar]
- C. Baiocchi, V. Komornik and P. Loreti, Ingham-Beurling type theorems with weakened gap conditions. Acta Math. Hungar. 97 (2002) 55–95. [CrossRef] [MathSciNet] [Google Scholar]
- R. Dáger and E. Zuazua, Wave propagation, observation and control in 1-d flexible multi-structures, Mathématiques & Applications 50. Springer-Verlag, Berlin (2006). [Google Scholar]
- R. Datko, Not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks. SIAM J. Control Optim. 26 (1988) 697–713. [CrossRef] [MathSciNet] [Google Scholar]
- R. Datko, Two examples of ill-posedness with respect to time delays revisited. IEEE Trans. Automat. Contr. 42 (1997) 511–515. [Google Scholar]
- R. Datko, J. Lagnese and M.P. Polis, An example on the effect of time delays in boundary feedback stabilization of wave equations. SIAM J. Control Optim. 24 (1986) 152–156. [CrossRef] [MathSciNet] [Google Scholar]
- K.P. Hadeler, Delay equations in biology, in Functional differential equations and approximation of fixed points, Lect. Notes Math. 730, Springer, Berlin (1979) 136–156. [Google Scholar]
- J. Hale and S. Verduyn Lunel, Introduction to functional differential equations, Applied Mathematical Sciences 99. Springer (1993). [Google Scholar]
- A.E. Ingham, Some trigonometrical inequalities with applications to the theory of series. Math. Z. 41 (1936) 367–379. [Google Scholar]
- I. Lasiecka, R. Triggiani and P.-F. Yao. Inverse/observability estimates for second-order hyperbolic equations with variable coefficients. J. Math. Anal. Appl. 235 (1999) 13–57. [CrossRef] [MathSciNet] [Google Scholar]
- H. Logemann, R. Rebarber and G. Weiss, Conditions for robustness and nonrobustness of the stability of feedback systems with respect to small delays in the feedback loop. SIAM J. Control Optim. 34 (1996) 572–600. [CrossRef] [MathSciNet] [Google Scholar]
- 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 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
- S. Nicaise and J. Valein, Stabilization of the wave equation on 1-D networks with a delay term in the nodal feedbacks. Netw. Heterog. Media 2 (2007) 425–479 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
- A. Pazy, Semigroups of linear operators and applications to partial differential equations. Appl. Math. Sci. 44 (1983). [Google Scholar]
- R. Rebarber, Exponential stability of coupled beams with dissipative joints: a frequency domain approach. SIAM J. Control Optim. 33 (1995) 1–28. [CrossRef] [MathSciNet] [Google Scholar]
- R. Rebarber and S. Townley, Robustness with respect to delays for exponential stability of distributed parameter systems. SIAM J. Control Optim. 37 (1999) 230–244. [CrossRef] [MathSciNet] [Google Scholar]
- I.H. Suh and Z. Bien, Use of time delay action in the controller design. IEEE Trans. Automat. Contr. 25 (1980) 600–603. [CrossRef] [Google Scholar]
- M. Tucsnak and G. Weiss, How to get a conservative well-posed linear system out of thin air. II. Controllability and stability. SIAM J. Control Optim. 42 (2003) 907–935. [CrossRef] [MathSciNet] [Google Scholar]
- 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 (electronic). [CrossRef] [EDP Sciences] [Google Scholar]
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