EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 31 (2025) ESAIM: COCV, 31 (2025) 17 References
Open Access
Issue
ESAIM: COCV
Volume 31, 2025
Article Number 17
Number of page(s) 39
DOI https://doi.org/10.1051/cocv/2024084
Published online 17 March 2025
  1. M. Badra and J.-P. Raymond, Approximation of feedback gains for the Oseen system. Preprint (2025). https://hal.science/hal-04880955. [Google Scholar]
  2. M. Badra and J.-P. Raymond, Numerical approximation of the Oseen system in polyhedral or polygonal domains. Preprint (2025). https://hal.science/hal-04880966. [Google Scholar]
  3. M. Badra and J.-P. Raymond, The Oseen system with nonhomogeneous boundary conditions in polyhedral or polygonal domains. Preprint (2025). https://hal.science/hal-04880963. [Google Scholar]
  4. M. Badra and J.-P. Raymond, Feedback stabilization of the Oseen system approximated by the pseudo-compressibility method, special issue of Mathematical Reports dedicated to Marius Tucsnak, Vol. 24 (2022) 39–57. [Google Scholar]
  5. M. Badra and J.-P. Raymond, Approximation of feedback gains using spectral projections: application to the Oseen system. SIAM J. Control Optim. 62 (2024) 2910–2935. [CrossRef] [MathSciNet] [Google Scholar]
  6. H.T. Banks and K. Kunisch, The linear regulator problem for parabolic systems. SIAM J. Control Optim. 22 (1984) 684–698. [CrossRef] [MathSciNet] [Google Scholar]
  7. M. Kroller and K. Kunisch, Convergence rates for the feedback operators arising in the linear quadratic regulator problem governed by parabolic equations. SIAM J. Numer. Anal. 28 (1991) 1350–1385. [CrossRef] [MathSciNet] [Google Scholar]
  8. I. Lasiecka, Convergence rates for the approximations of the solutions to algebraic Riccati equations with unbounded coefficients: case of analytic semigroups. Numer. Math. 63 (1992) 357–390. [CrossRef] [MathSciNet] [Google Scholar]
  9. I. Lasiecka and R. Triggiani, The regulator problem for parabolic equations with Dirichlet boundary control. II. Galerkin approximation. Appl. Math. Optim. 16 (1987) 187–216. [CrossRef] [MathSciNet] [Google Scholar]
  10. I. Lasiecka and R. Triggiani, Numerical approximations of algebraic Riccati equations for abstract systems modelled by analytic semigroups, and applications. Math. Comp. 57 (1991) 639–662, S13–S37. [Google Scholar]
  11. I. Lasiecka and R. Triggiani, Control theory for partial differential equations: continuous and approximation theories. I. Abstract parabolic systems, Vol. 74 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (2000). [Google Scholar]
  12. H.T. Banks and K. Ito, Approximation in LQR problems for infinite-dimensional systems with unbounded input operators. J. Math. Syst. Estim. Control 7 (1997) 1–34. [Google Scholar]
  13. T. Kato, Perturbation Theory for Linear Operators, Classics in Mathematics. Springer-Verlag, Berlin (1995). [CrossRef] [Google Scholar]
  14. J.S. Gibson, An analysis of optimal modal regulation: convergence and stability. SIAM J. Control Optim. 19 (1981) 686–707. [CrossRef] [MathSciNet] [Google Scholar]
  15. J.S. Gibson and A. Adamian, Approximation Theory for Linear-Quadratic-Gaussian Optimal Control of Flexible Structures. SIAM J. Control Optim. 29 (1991) 1–37. [CrossRef] [MathSciNet] [Google Scholar]
  16. F. Kappel and D. Salamon, An approximation theorem for the algebraic Riccati equation. SIAM J. Control Optim. 28 (1990) 1136–1147. [CrossRef] [MathSciNet] [Google Scholar]
  17. K. Ramdani, T. Takahashi and M. Tucsnak, Uniformly exponentially stable approximations for a class of second order evolution equations—application to LQR problems. ESAIM Control Optim. Calc. Var. 13 (2007) 503–527. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  18. H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, 2nd edn. Johann Ambrosius Barth, Heidelberg (1995). [Google Scholar]
  19. A. Bensoussan, G. Da Prato, M.C. Delfour and S.K. Mitter, Representation and control of infinite dimensional systems, Systems & Control: Foundations & Applications, 2nd edn. Birkhauser Boston Inc., Boston, MA (2007). [CrossRef] [Google Scholar]
  20. A. Pazy, Semigroups of linear operators and applications to partial differential equations. Vol. 44 of Applied Mathematical Sciences. Springer-Verlag, New York (1983). [Google Scholar]
  21. K. Ito and F. Kappel, The Trotter-Kato theorem and approximation of PDEs. Math. Comp. 67 (1998) 21–44. [CrossRef] [MathSciNet] [Google Scholar]
  22. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York (2011). [CrossRef] [Google Scholar]
  23. J. Bergh and J. Löfström, Interpolation Spaces. An Introduction. Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, Berlin-New York (1976). [Google Scholar]
  24. J. Zabczyk, Mathematical Control Theory. Modern Birkhäuser Classics. Birkhäuser Boston, Inc., Boston, MA (2008). [CrossRef] [Google Scholar]
  25. R. Triggiani, A sharp result on the exponential operator-norm decay of a family Th (t) of strongly continuous semigroups uniformly in h, in Optimal control of differential equations (Athens, OH, 1993). Vol. 160 of Lecture Notes in Pure and Applied Mathematics. Dekker, New York (1994) 325–335. [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.