EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 32 (2026) ESAIM: COCV, 32 (2026) 1 References
Open Access
Issue
ESAIM: COCV
Volume 32, 2026
Article Number 1
Number of page(s) 32
DOI https://doi.org/10.1051/cocv/2024093
Published online 21 January 2026
  1. J.-M. Coron, Control and Nonlinearity, Mathematical Surveys and Monographs, Vol. 136. American Mathematical Society, Providence, RI (2007). MR 2302744 [Google Scholar]
  2. M. Tucsnak and G. Weiss, Observation and Control for Operator Semigroups, Birkhäuser Advanced Texts: Basler Lehrbücher [Birkhauser Advanced Texts: Basel Textbooks]. Birkhauser Verlag, Basel (2009). MR 2502023 [Google Scholar]
  3. J.-L. Lions, Optimal control of systems governed by partial differential equations, Die Grundlehren der mathematischen Wissenschaften, Band 170. Springer-Verlag, New York-Berlin (1971). Translated from the French by S.K. Mitter. MR 271512 [Google Scholar]
  4. M. Slemrod, A note on complete controllability and stabilizability for linear control systems in Hilbert space. SIAM J. Control 12 (1974) 500–508. MR 353107 [CrossRef] [MathSciNet] [Google Scholar]
  5. R.F. Curtain and H. Zwart, An Introduction to Infinite-dimensional Linear Systems Theory, Texts in Applied Mathematics, Vol. 21. Springer-Verlag, New York (1995). MR 1351248 [Google Scholar]
  6. G. Weiss and H. Zwart, An example in linear quadratic optimal control. Syst. Control Lett. 33 (1998) 339–349. MR 1623882 [CrossRef] [Google Scholar]
  7. K.-J. Engel and R. Nagel, One-parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics, Vol. 194. Springer-Verlag, New York (2000). With contributions by S. Brendle, M. Campiti, T. Hahn, G. Metafune, G. Nickel, D. Pallara, C. Perazzoli, A. Rhandi, S. Romanelli and R. Schnaubelt. MR 1721989 [Google Scholar]
  8. J. Zabczyk, Mathematical Control Theory. Modern Birkhäauser Classics, Birkhäauser Boston, Inc., Boston, MA (2008). An introduction, Reprint of the 1995 edition. MR 2348543 [Google Scholar]
  9. E. Trelat, G. Wang and Y. Xu, Characterization by observability inequalities of controllability and stabilization properties. Pure Appl. Anal. 2 (2020) 93–122. MR 4041279 [CrossRef] [MathSciNet] [Google Scholar]
  10. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Universitext. Springer, New York (2011). MR 2759829 [Google Scholar]
  11. F. Flandoli, I. Lasiecka and R. Triggiani, Algebraic Riccati equations with nonsmoothing observation arising in hyperbolic and Euler-Bernoulli boundary control problems. Ann. Mat. Pura Appl. 153 (1988) 307–382. MR 1008349 [Google Scholar]
  12. A.J. Pritchard and D.A. Salamon, The linear quadratic control problem for infinite-dimensional systems with unbounded input and output operators. SIAM J. Control Optim. 25 (1987) 121–144. MR 872455 [Google Scholar]
  13. F. Flandoli, A new approach to the lqr problem for hyperbolic dynamics with boundary control. Distributed Parameter Systems: Proceedings of the 3rd International Conference. Vorau, Styria, July 6-12, 1986. Springer (1987) 89–111. [Google Scholar]
  14. I. Lasiecka and R. Triggiani, Differential and Algebraic Riccati Equations with Application to Boundary/Point Control Problems: Continuous Theory and Approximation Theory. Lecture Notes in Control and Information Sciences, Vol. 164. Springer-Verlag, Berlin (1991). MR 1132440 [Google Scholar]
  15. G. Weiss and R. Rebarber, Optimizability and estimatability for infinite-dimensional linear systems. SIAM J. Control Optim. 39 (2000) 1204–1232. MR 1814273 [Google Scholar]
  16. H. Zwart, Linear Quadratic Optimal Control for Abstract Linear Systems. Modelling and Optimization of Distributed Parameter Systems (Warsaw, 1995). Chapman & Hall, New York (1996) 175–182. MR 1388531 [Google Scholar]
  17. O. Staffans, Well-posed Linear Systems. Encyclopedia of Mathematics and its Applications, Vol. 103. Cambridge University Press, Cambridge (2005). MR 2154892 [Google Scholar]
  18. V. Komornik, Rapid boundary stabilization of linear distributed systems. SIAM J. Control Optim. 35 (1997) 1591–1613. MR 1466918 [Google Scholar]
  19. A. Vest, Rapid stabilization in a semigroup framework. SIAM J. Control Optim. 51 (2013) 4169–4188. MR 3120757 [Google Scholar]
  20. D.L. Lukes, Stabilizability and optimal control. Funkcial. Ekvac. 11 (1968) 39–50. MR 238589 [Google Scholar]
  21. D. Kleinman, An easy way to stabilize a linear constant system. IEEE Trans. Automatic Control 15 (1970) 692–692. [Google Scholar]
  22. J.M. Urquiza, Rapid exponential feedback stabilization with unbounded control operators. SIAM J. Control Optim. 43 (2005) 2233–2244. MR 2179485 [CrossRef] [MathSciNet] [Google Scholar]
  23. D.L. Russell, Mathematics of Finite-dimensional Control Systems. Lecture Notes in Pure and Applied Mathematics, Vol. 43. Marcel Dekker, Inc., New York (1979). MR 531035 [Google Scholar]
  24. J.-M. Coron and H.-M. Nguyen, Null controllability and finite time stabilization for the heat equations with variable coefficients in space in one dimension via backstepping approach. Arch. Rational Mech. Anal. 225 (2017) 993–1023. [Google Scholar]
  25. H.-M. Nguyen, Rapid stabilization and finite time stabilization of the bilinear Schrödinger equation (2024), submitted, https://arxiv.org/abs/2405.10002. [Google Scholar]
  26. H.-M. Nguyen, Rapid and finite-time boundary stabilization of a KdV system. SIAM J. Control and Optimization, to appear, https://arxiv.org/abs/2409.11768. [Google Scholar]
  27. E.D. Sontag, Mathematical Control Theory, 2ndedn. Texts in Applied Mathematics, Vol. 6. Springer-Verlag, New York (1998). MR 1640001 [Google Scholar]
  28. J.-M. Coron and L. Praly, Adding an integrator for the stabilization problem. Syst. Control Lett. 17 (1991) 89–104. MR MR1120754 (92f:93099) [Google Scholar]
  29. J.-M. Coron, R. Vazquez, M. Krstic and G. Bastin, Local exponential H2 stabilization of a 2 x 2 quasilinear hyperbolic system using backstepping. SIAM J. Control Optim. 51 (2013) 2005–2035. MR 3049647 [CrossRef] [MathSciNet] [Google Scholar]
  30. J.-M. Coron and H.-M. Nguyen, Lyapunov functions and finite-time stabilization in optimal time for homogeneous linear and quasilinear hyperbolic systems. Ann. Inst. H. Poincare C Anal. Non Linéaire 39 (2022) 1235–1260. MR 4515096 [Google Scholar]
  31. A. Bensoussan, G. Da Prato, M.C. Delfour and S.K. Mitter, Representation and Control of Infinite Dimensional Systems, 2nd edn. Systems & Control: Foundations & Applications. Birkhauser Boston, Inc., Boston, MA (2007). MR 2273323 [Google Scholar]
  32. J.M. Ball, Strongly continuous semigroups, weak solutions, and the variation of constants formula. Proc. Amer. Math. Soc. 63 (1977) 370–373. MR 442748 [MathSciNet] [Google Scholar]
  33. V. Barbu, I. Lasiecka and R. Triggiani, Extended Algebraic Riccati Equations in the Abstract Hyperbolic Case, Vol. 40. Lakshmikantham's Legacy: A Tribute on his 75th Birthday (2000) 105–129. MR 1768405 [Google Scholar]
  34. R. Triggiani, The dual algebraic Riccati equations: additional results under isomorphism of the Riccati operator. Appl. Math. Lett. 18 (2005) 1001–1008. MR 2156994 [Google Scholar]
  35. P. Grabowski, On the spectral-Lyapunov approach to parametric optimization of distributed-parameter systems. IMA J. Math. Control Inform. 7 (1990) 317–338. MR 1099758 [Google Scholar]
  36. S. Hansen and G. Weiss, New Results on the Operator Carleson Measure Criterion, Vol. 14. Distributed Parameter Systems: Analysis, Synthesis and Applications, Part 1 (1997) 3–32. MR 1446962 [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.