Open Access
Issue
ESAIM: COCV
Volume 27, 2021
Article Number 94
Number of page(s) 30
DOI https://doi.org/10.1051/cocv/2021090
Published online 06 October 2021
  1. B. d’Andréa-Novel, F. Boustany, F. Conrad and B.P. Rao, Feedback stabilization of a hybrid PDE-ODE system: application to an overhead crane. MCSS J. 7 (1994) 1–22. [Google Scholar]
  2. B. d’Andréa-Novel and J.-M. Coron, Exponential stabilization of an overhead crane with flexible cable via a back-stepping approach. Automatica 36 (2000) 587–593. [Google Scholar]
  3. B. d’Andréa-Novel and J.-M. Coron, Stabilization of an overhead crane with a variable length flexible cable. Comput. Appl. Math. 21 (2002) 101–134. [Google Scholar]
  4. B. d’Andréa-Novel, B. Fabre and J.-M. Coron, An acoustic model for automatic control of a slide flute. Acta Acustica united with Acustica 96 (2010) 713–721. [Google Scholar]
  5. B. d’Andréa-Novel, I. Moyano and L. Rosier, Finite-time stabilization of an overhead crane with a flexible cable. Math. Control Signals Syst. 31 (2019) 6. [Google Scholar]
  6. F. Alabau-Boussouira, V. Perrollaz and L. Rosier, Finite-time stabilization of a network of strings. Math. Control Related Fields 5 (2015) 721–742. [Google Scholar]
  7. H. Anfinsen and O.M. Aamo, Adaptative Control of Hyperbolic PDEs. Springer (2019). [Google Scholar]
  8. A. Bacciotti and L. Rosier, Liapunov Functions and Stability in Control Theory, 2nd edn, Springer-Verlag, Berlin, Heidelberg (2005). [Google Scholar]
  9. S.P. Bhat and D.S. Bernstein, Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38 (2000) 751–766. [Google Scholar]
  10. J.-M. Coron, Control and Nonlinearity. Vol. 136 of Mathematical Surveys and Monographs. American Mathematical Society (2007). [Google Scholar]
  11. J.-M. Coron and B. d’Andréa-Novel, Stabilization of a rotating body-beam without damping. IEEE Trans. Automatic Control 43 (1998) 608–618. [Google Scholar]
  12. J.-M. Coron, R. Vazquez, M. Krstic and G. Bastin, Local exponential H2 stabilization of a 2 × 2 quasilinear hyperbolic system using backstepping. SIAM J. Control Optim. 51 (2013) 2005–2035. [Google Scholar]
  13. J. Daafouz, M. Tucsnak and J. Valein, Nonlinear control of a coupled PDE/ODE system modeling a switched power converter with a transmission line. Syst. Control Lett. 70 (2014) 92–99. [Google Scholar]
  14. M. Gugat, V. Perrollaz and L. Rosier, Boundary stabilization of quasilinear hyperbolic systems of balance laws: exponential decay for small source terms. J. Evol. Equ. 18 (2018) 1471–1500. [Google Scholar]
  15. V.T. Haimo, Finite time controllers. SIAM J. Control Optim. 24 (1986) 760–770. [Google Scholar]
  16. M. Krstic and A. Smyshlyaev, Boundary control of PDEs – A course on backstepping designs. SIAM (2008). [Google Scholar]
  17. G. Leugering and E.J.P.G. Schmidt, On the modelling and stabilization of flows in networks of open canals. SIAM J. Control Optim. 41 (2002) 164–180. [Google Scholar]
  18. A. Majda and R. Phillips, Disappearing solutions for the dissipative wave equations. Indiana Univ. Math. J. 24 (1975) 1119–1133. [Google Scholar]
  19. P. Martin, L. Rosier and P. Rouchon, Null controllability of one-dimensional parabolic equations by the flatness approach. SIAM J. Control Optim. 54 (2016) 198–220. [Google Scholar]
  20. A. Mattioni, Y. Wu, Y. Le Gorrec and H. Zwart, Stabilisation of a rotating beam clamped on a moving inertia with strong dissipation feedback, in Proceedings of the 59th IEEE Conference on Decision and Control, Jeju Island (2020) 5056–5061. [Google Scholar]
  21. A. Mifdal, Stabilisation uniforme d’un système hybride. C.R. Acad. Sci. Paris, t. 324, Série I (1997) 37–42. [Google Scholar]
  22. J.J. Moré, B.S. Garbow and K.E. Hillstrom, User guide for MINPACK-1. Argonne National Laboratory (1980). [Google Scholar]
  23. O. Morgül, B.P. Rao and F. Conrad, On the stabilization of a cable with a tip mass. IEEE Trans. Autom. Control 39 (1994) 440–454. [Google Scholar]
  24. V. Perrollaz and L. Rosier. Finite-time stabilization of 2 × 2 hyperbolic systems on tree-shaped networks. SIAM J. Control Optim. 52 (2014) 143–163. [Google Scholar]
  25. A. Polyakov, Fixed-time stabilization of linear systems via sliding mode control, in 2012 12th International Workshop on Variable Structure Systems, IEEE (2012) 1–6. [Google Scholar]
  26. A. Polyakov, Sliding mode control design using canonical homogeneous norm. Int. J. Robust Nonlinear Control 29 (2019) 682–701. [Google Scholar]
  27. A. Polyakov, D. Efimov and B. Brogliato, Consistent discretization of finite-time and fixed-time stable systems. SIAM J. Control Optim. 57 (2019) 78–103. [Google Scholar]
  28. L. Sainsaulieu, Calcul scientifique. Masson (1996). [Google Scholar]
  29. R. Sepulchre, M. Janković and P. Kokotović, Constructive Nonlinear Control. Springer-Verlag (1997). [Google Scholar]
  30. Y. Shang, D. Liu and G. Xu, Super-stability and the spectrum of one-dimensional wave equations on general feedback controlled networks. IMA J. Math. Control Inform. 31 (2014) 73–90. [Google Scholar]
  31. N.-T. Trinh, V. Andrieu and C.-Z. Xu, Design of integral controllers for nonlinear systems governed by scalar hyperbolic partial differential equations. IEEE Trans. Autom. Control 62 (2017) 4527–4536. [Google Scholar]
  32. R. Vazquez and M. Krstic, Marcum Q-functions and explicit kernels for stabilization of 2 × 2 linear hyperbolic systems with constant coefficients. Syst. Control Lett. 68 (2014) 33–42. [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.