Open Access
Volume 29, 2023
Article Number 72
Number of page(s) 30
Published online 08 September 2023
  1. H.T. Banks, K. Ito and C. Wang, Exponentially stable approximations of weakly damped wave equations. Int. Ser. Numer. Math. 100 (1991) 1–33. [CrossRef] [Google Scholar]
  2. H.El. Boujaoui, H. Bouslous and L. Maniar, Boundary stabilization for 1-D semidiscrete wave equation by filtering technique. Bull. TICMI 17 (2013) 1–18. [MathSciNet] [Google Scholar]
  3. R.H. Cannon and E. Schmitz, Initial experiments on the end-point control of a flexible one-link robot. Int. J. Robot. Res. 3 (1984) 62–75. [CrossRef] [Google Scholar]
  4. P.A. Chodavarapu and M.W. Spong, On noncollocated control of a single flexible link. Proc. IEEE Int. Conf. Robotics Automation (1996) 1101–1106. [CrossRef] [Google Scholar]
  5. C. Castro and S. Micu, Boundary controllability of a linear semi-discrete 1-D wave equation derived from a mixed finite element method. Numer. Math. 102 (2006) 413–462. [CrossRef] [MathSciNet] [Google Scholar]
  6. B.Z. Guo and C.Z. Xu, On the spectrum-determined growth condition of a vibration cable with a tip mass. IEEE Trans. Autom. Control 45 (2000) 89–93. [CrossRef] [Google Scholar]
  7. B.Z. Guo and B.B. Xu, A semi-discrete finite difference method to uniform stabilization of wave equation with local viscosity. IFAC J. Syst. Control 13 (2020) 100100. [CrossRef] [MathSciNet] [Google Scholar]
  8. B.Z. Guo and J.M. Wang, Control of Wave and Beam PDEs The Riesz Basis Approach. Springer-Verlag, Cham (2019). [CrossRef] [Google Scholar]
  9. I.C. Gohberg and M.G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators. Providence, RI (1969). [Google Scholar]
  10. R. Glowinski, W. Kinton and M.F. Wheeler, A mixed finite element formulation for the boundary controllability of the wave equation. Int. J. Numer. Methods Biomed. Eng. 27 (1989) 623–635. [CrossRef] [Google Scholar]
  11. J.A. Infante and E. Zuazua, Boundary observability for the space semi-discretizations of the 1-D wave equation. ESAIM Math. Model. Numer. Anal. 33 (1999) 407–438. [CrossRef] [EDP Sciences] [Google Scholar]
  12. P. Loreti and M. Mehrenberger, An ingham type proof for a two-grid observability theorem. ESAIM Control Optim. Calc. Var. 14 (2008) 604–631. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  13. J. Liu, R. Hao and B.Z. Guo, Order reduction-based uniform approximation of exponential stability for one-dimensional Schrödinger equation. Syst. Control Lett. 160 (2022) 105136. [CrossRef] [Google Scholar]
  14. J. Liu and B.Z. Guo, A new semidiscretized order reduction finite difference scheme for uniform approximation of one-dimensional wave equation. SIAM J. Control Optim. 58 (2020) 2256–2287. [CrossRef] [MathSciNet] [Google Scholar]
  15. J. Liu and B.Z. Guo, A novel semi-discrete scheme preserving uniformly exponential stability for an Euler Cbernoulli beam. Syst. Control Lett. 134 (2019) 104518. [CrossRef] [Google Scholar]
  16. J. Liu and B.Z. Guo, Uniformly semidiscretized approximation for exact observability and controllability of one-dimensional Euler–Bernoulli beam. Syst. Control Lett. 156 (2021) 105013. [CrossRef] [Google Scholar]
  17. W. Lacarbonara and H. Yabuno, Closed-loop non-linear control of an initially imperfect beam with non-collocated input. J. Sound Vibrat. 273 (2004) 695–711. [CrossRef] [Google Scholar]
  18. O. Morgul, B. Rao and F. Conrad, On the stabilization of a cable with a tip mass. IEEE Trans. Automat. Control 39 (1994) 2140–2145. [CrossRef] [MathSciNet] [Google Scholar]
  19. Z.D. Mei, Output feedback exponential stabilization for a 1-D wave PDE with dynamic boundary. J. Math. Anal. Appl. 508 (2022) 125860. [CrossRef] [Google Scholar]
  20. M. Negreanu and E. Zuazua, Uniform boundary controllability of a discrete 1-D wave equation. Syst. Control Lett. 48 (2003) 261–279. [CrossRef] [Google Scholar]
  21. H.J. Ren and B.Z. Guo, Uniformly exponential stability of semi-discrete scheme for observer-based control of 1-D wave equation. Syst. Control Lett. 168 (2022) 105346. [CrossRef] [Google Scholar]
  22. L.T. Tebou and E. Zuazua, Uniform boundary stabilization of the finite difference space discretization of the 1-d wave equation. Adv. Comput. Math. 26 (2007) 337–365. [CrossRef] [MathSciNet] [Google Scholar]
  23. E. Zuazua, Propagation, observation, and control of waves approximated by finite difference methods. SIAM Rev. 47 (2005) 197–243. [CrossRef] [MathSciNet] [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.