Free Access
Issue
ESAIM: COCV
Volume 18, Number 1, January-March 2012
Page(s) 22 - 35
DOI https://doi.org/10.1051/cocv/2010044
Published online 02 December 2010
  1. R.F. Curtain, The Salamon-Weiss class of well-posed infinite dimensional linear systems : a survey. IMA J. Math. Control Inform. 14 (1997) 207–223. [CrossRef] [MathSciNet] [Google Scholar]
  2. R. Datko, Two questions concerning the boundary control of certain elastic systems. J. Diff. Equ. 92 (1991) 27–44. [CrossRef] [Google Scholar]
  3. R. Datko, Is boundary control a realistic approach to the stabilization of vibrating elastic systems?, in Evolution Equations, Baton Rouge (1992), Lecture Notes in Pure and Appl. Math. 168, Dekker, New York (1995) 133–140. [Google Scholar]
  4. R. Datko, Two examples of ill-posedness with respect to time delays revisited. IEEE Trans. Automat. Control 42 (1997) 511–515. [CrossRef] [MathSciNet] [Google Scholar]
  5. R. Datko and Y.C. You, Some second-order vibrating systems cannot tolerate small time delays in their damping. J. Optim. Theory Appl. 70 (1991) 521–537. [CrossRef] [MathSciNet] [Google Scholar]
  6. 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]
  7. A.J. Deguenon, G. Sallet and C.Z. Xu, A Kalman observer for infinite-dimensional skew-symmetric systems with application to an elastic beam, Proc. of the Second International Symposium on Communications, Control and Signal Processing, Marrakech, Morocco (2006). [Google Scholar]
  8. W.H. Fleming Ed., Future Directions in Control Theory. SIAM, Philadelphia (1988). [Google Scholar]
  9. I. Gumowski and C. Mira, Optimization in Control Theory and Practice. Cambridge University Press, Cambridge (1968). [Google Scholar]
  10. B.Z. Guo and Y.H. Luo, Controllability and stability of a second order hyperbolic system with collocated sensor/actuator. Syst. Control Lett. 46 (2002) 45–65. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  11. B.Z. Guo and Z.C. Shao, Stabilization of an abstract second order system with application to wave equations under non-collocated control and observations. Syst. Control Lett. 58 (2009) 334–341. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  12. B.Z. Guo and C.Z. Xu, The stabilization of a one-dimensional wave equation by boundary feedback with non-collocated observation. IEEE Trans. Automat. Contr. 52 (2007) 371–377. [CrossRef] [Google Scholar]
  13. B.Z. Guo and K.Y. Yang, Dynamic stabilization of an Euler-Bernoulli beam equation with time delay in boundary observation. Automatica 45 (2009) 1468–1475. [CrossRef] [MathSciNet] [Google Scholar]
  14. B.Z. Guo, J.M. Wang and K.Y. Yang, Dynamic stabilization of an Euler-Bernoulli beam under boundary control and non-collocated observation. Syst. Control Lett. 57 (2008) 740–749. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  15. I. Lasiecka and R. Triggiani, Control Theory for Partial Differential Equations : Continuous and Approxiamation Theories – II : Abstract Hyperbolic-Like Systems over a Finite Time Horizon. Cambridge University Press, Cambridge (2000). [Google Scholar]
  16. 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]
  17. 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] [Google Scholar]
  18. F. Oberhettinger and L. Badii, Tables of Laplace Transforms. Springer-Verlag, Berlin (1973). [Google Scholar]
  19. A. Smyshlyaev and M. Krstic, Backstepping observers for a class of parabolic PDEs. Syst. Control Lett. 54 (2005) 613–625. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  20. L.N. Trefethen, Spectral Methods in Matlab. SIAM, Philadelphia (2000). [Google Scholar]
  21. M. Tucsnak and G. Weiss, Observation and Control for Operator Semigroups. Birkhäuser, Basel (2009). [Google Scholar]

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.