Free Access
Volume 12, Number 4, October 2006
Page(s) 770 - 785
Published online 11 October 2006
  1. I. Gumowski and C. Mira, Optimization in Control Theory and Practice. Cambridge University Press, Cambridge (1968).
  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.
  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.
  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]
  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]
  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.
  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.
  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.
  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]
  10. J.K. Hale and S.M. Verduyn-Lunel, Introduction to functional differential equations, in Applied Mathematical Sciences, New York, Springer 99 (1993).
  11. S.I. Niculescu and R. Lozano, On the passivity of linear delay systems. IEEE Trans. Automat. Control 46 (2001) 460–464. [CrossRef] [MathSciNet]
  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.
  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]
  14. Ö. Mörgul, Stabilization and disturbance rejection for the wave equation. IEEE Trans. Automat. Control 43 (1998) 89–95. [CrossRef] [MathSciNet]
  15. J.-L. Lions, Exact controllability, stabilization and perturbations for distributed parameter system. SIAM Rev. 30 (1988) 1–68. [CrossRef] [MathSciNet]
  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]
  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]
  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]
  19. I.C. Gohberg and M.G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators. AMS Transl. Math. Monographs 18 (1969).
  20. Lars V. Ahlfors, Complex Analysis. McGraw-Hill.

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.