 C. Abdallah, P. Dorato, J. BenitezRead and R. Byrne, Delayed positive feedback can stabilize oscillatory systems, in ACC' 93 (American Control Conference), San Francisco (1993) 3106–3107.
 K. Ammari and M. Tucsnak, Stabilization of BernoulliEuler beams by means of a pointwise feedback force. SIAM J. Control Optim. 39 (2000) 1160–1181 (electronic). [CrossRef] [MathSciNet]
 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]
 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).
 W. Arendt and C.J.K. Batty, Tauberian theorems and stability of oneparameter semigroups. Trans. Amer. Math. Soc. 305 (1988) 837–852. [CrossRef] [MathSciNet]
 C. Baiocchi, V. Komornik and P. Loreti, InghamBeurling type theorems with weakened gap conditions. Acta Math. Hungar. 97 (2002) 55–95. [CrossRef] [MathSciNet]
 R. Dáger and E. Zuazua, Wave propagation, observation and control in 1d flexible multistructures, Mathématiques & Applications 50. SpringerVerlag, Berlin (2006).
 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]
 R. Datko, Two examples of illposedness with respect to time delays revisited. IEEE Trans. Automat. Contr. 42 (1997) 511–515. [CrossRef] [MathSciNet]
 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]
 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.
 J. Hale and S. Verduyn Lunel, Introduction to functional differential equations, Applied Mathematical Sciences 99. Springer (1993).
 A.E. Ingham, Some trigonometrical inequalities with applications to the theory of series. Math. Z. 41 (1936) 367–379. [CrossRef] [MathSciNet]
 I. Lasiecka, R. Triggiani and P.F. Yao. Inverse/observability estimates for secondorder hyperbolic equations with variable coefficients. J. Math. Anal. Appl. 235 (1999) 13–57. [CrossRef] [MathSciNet]
 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]
 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]
 S. Nicaise and J. Valein, Stabilization of the wave equation on 1D networks with a delay term in the nodal feedbacks. Netw. Heterog. Media 2 (2007) 425–479 (electronic). [CrossRef] [MathSciNet]
 A. Pazy, Semigroups of linear operators and applications to partial differential equations. Appl. Math. Sci. 44 (1983).
 R. Rebarber, Exponential stability of coupled beams with dissipative joints: a frequency domain approach. SIAM J. Control Optim. 33 (1995) 1–28. [CrossRef] [MathSciNet]
 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]
 I.H. Suh and Z. Bien, Use of time delay action in the controller design. IEEE Trans. Automat. Contr. 25 (1980) 600–603. [CrossRef]
 M. Tucsnak and G. Weiss, How to get a conservative wellposed linear system out of thin air. II. Controllability and stability. SIAM J. Control Optim. 42 (2003) 907–935. [CrossRef] [MathSciNet]
 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]
Free access
Issue 
ESAIM: COCV
Volume 16, Number 2, AprilJune 2010



Page(s)  420  456  
DOI  http://dx.doi.org/10.1051/cocv/2009007  
Published online  21 April 2009 