Free Access
Issue
ESAIM: COCV
Volume 12, Number 4, October 2006
Page(s) 770 - 785
DOI https://doi.org/10.1051/cocv:2006021
Published online 11 October 2006
  1. I. Gumowski and C. Mira, Optimization in Control Theory and Practice. Cambridge University Press, Cambridge (1968). [Google Scholar]
  2. R. Datko, J. Lagness and M.P. Poilis, An example on the effect of time delays in boundary feedback stabilization of wave equations. SIAM J. Control Optim. 24 (1986) 152–156. [Google Scholar]
  3. R. Datko, Not all feedback stabilized hyperbolic systems are robust with respect to small time delay in their feedbacks. SIAM J. Control Optim. 26 (1988) 697–713. [Google Scholar]
  4. I.H. Suh and Z. Bien, Use of time delay action in the controller design. IEEE Trans. Automat. Control 25 (1980) 600–603. [CrossRef] [Google Scholar]
  5. 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]
  6. G. 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]
  7. N. Jalili and N. Olgac, Optimum delayed feedback vibration absorber for MDOF mechanical structure, in 37th IEEE CDC'98 (Conference on decision and control), Tampa, FL, December (1998) 4734–4739. [Google Scholar]
  8. W. Aernouts, D. Roose and R. Sepulchre, Delayed control of a Moore-Greitzer axial compressor model. Intern. J. Bifurcation Chaos 10 (2000) 115–1164. [Google Scholar]
  9. J.K. Hale and S.M. Verduyn-Lunel, Strong stabilization of neutral functional differential equations. IMA J. Math. Control Inform. 19 (2002) 5–24. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  10. J.K. Hale and S.M. Verduyn-Lunel, Introduction to functional differential equations, in Applied Mathematical Sciences, New York, Springer 99 (1993). [Google Scholar]
  11. S.I. Niculescu and R. Lozano, On the passivity of linear delay systems. IEEE Trans. Automat. Control 46 (2001) 460–464. [CrossRef] [MathSciNet] [Google Scholar]
  12. P. Borne, M. Dambrine, W. Perruquetti and J.P. Richard, Vector Lyapunov functions: nonlinear, time-varying, ordinary and functional differential equations. Stability and control: theory, methods and applications 13, Taylor and Francis, London (2003) 49–73. [Google Scholar]
  13. Ö. Mörgul, On the stabilization and stability robustness against small delays of some damped wave equation. IEEE Trans. Automat. Control 40 (1995) 1626–1630. [CrossRef] [MathSciNet] [Google Scholar]
  14. Ö. Mörgul, Stabilization and disturbance rejection for the wave equation. IEEE Trans. Automat. Control 43 (1998) 89–95. [CrossRef] [MathSciNet] [Google Scholar]
  15. J.-L. Lions, Exact controllability, stabilization and perturbations for distributed parameter system. SIAM Rev. 30 (1988) 1–68. [CrossRef] [MathSciNet] [Google Scholar]
  16. G.Q. Xu and B.Z. Guo, Riesz basis property of evolution equations in Hilbert spaces and application to a coupled string equation. SIAM J. Control Optim. 42 (2003) 966–984. [CrossRef] [MathSciNet] [Google Scholar]
  17. M.A. Shubov, The Riesz basis property of the system of root vectors for the equation of a nonhomogeneous damped string: transformation operators method. Methods Appl. Anal. 6 (1999) 571–591. [MathSciNet] [Google Scholar]
  18. G.Q. Xu and S.P. Yung, The expansion of semigroup and a criterion of Riesz basis. J. Differ. Equ. 210 (2005) 1–24. [CrossRef] [Google Scholar]
  19. I.C. Gohberg and M.G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators. AMS Transl. Math. Monographs 18 (1969). [Google Scholar]
  20. Lars V. Ahlfors, Complex Analysis. McGraw-Hill. [Google Scholar]

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