Free Access
Issue
ESAIM: COCV
Volume 25, 2019
Article Number 82
Number of page(s) 31
DOI https://doi.org/10.1051/cocv/2018059
Published online 19 December 2019
  1. A.B. Aw and M. Rascle, Resurrection of “second order” models of traffic flow. SIAM J. Appl. Math. 60 (2000) 916–938. [Google Scholar]
  2. G. Bastin and J.-M. Coron, On boundary feedback stabilization of non-uniform linear 2 × 2 hyperbolic systems over a bounded interval. Syst. Control Lett. 60 (2011) 900–906. [Google Scholar]
  3. G. Bastin and J.-M. Coron, Stability and Boundary Stabilization of 1-D Hyperbolic Systems. Vol. 88 of Progress in Nonlinear Differential Equations Subseries in Control. Birkhäuser/Springer, Cham (2016). [Google Scholar]
  4. G. Bastin and J.-M. Coron, A quadratic Lyapunov function for hyperbolic density-velocity systems with nonuniform steady states. Syst. Control Lett. 104 (2017) 66–71. [Google Scholar]
  5. G. Bastin, J.-M. Coron and S.O. Tamasoiu, Stability of linear density-flow hyperbolic systems under PI boundary control. Automatica J. IFAC 53 (2015) 37–42. [CrossRef] [Google Scholar]
  6. H. Chanson, Hydraulics of Open Channel Flow. Butterworth- (2004). [Google Scholar]
  7. J.-M. Coron and G. Bastin, Dissipative boundary conditions for one-dimensional quasi-linear hyperbolic systems: Lyapunov stability for the C1-norm. SIAM J. Control Optim. 53 (2015) 1464–1483. [Google Scholar]
  8. J.-M. Coron, B. d’Andrea Novel and G. Bastin, Penser globalement, agir localement. Recherche-Paris 417 (2008) 82. [Google Scholar]
  9. 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]
  10. J. de Halleux, C. Prieur, J.-M. Coron, B. d’Andréa Novel and G. Bastin, Boundary feedback control in networks of open channels. Automatica J. IFAC 39 (2003) 1365–1376. [CrossRef] [MathSciNet] [Google Scholar]
  11. P.M. Dower and P.M. Farrell, On linear control of backward pumped Raman amplifiers. Vol. 39 of IFAC Proceedings (2006) 547–552. [CrossRef] [Google Scholar]
  12. P. Hartman, Ordinary Differential Equations. John Wiley & Sons, Inc., New York London, Sydney (1964). [Google Scholar]
  13. A. Hayat, Exponential stability of general 1-D quasilinear systems with source terms for the C1 norm under boundary conditions. Preprint (2017). [Google Scholar]
  14. A. Hayat and P. Shang, A quadratic Lyapunov function for Saint-Venant equations with arbitrary friction and space-varying slope. Automatica 100 (2019) 52–60. [CrossRef] [Google Scholar]
  15. M. Krstic and A. Smyshlyaev, Boundary Control of PDEs: A Course on Backstepping Designs, Vol. 16. SIAM (2008). [CrossRef] [Google Scholar]
  16. T.T. Li, Global Classical Solutions for Quasilinear Hyperbolic Systems. Vol. 32 of RAM: Research in Applied Mathematics. Masson, Paris; John Wiley & Sons, Ltd., Chichester (1994). [Google Scholar]
  17. T.T. Li and W.C. Yu, Boundary Value Problems for Quasilinear Hyperbolic Systems. Duke University Mathematics Series. V. Duke University, Mathematics Department, Durham, NC (1985). [Google Scholar]
  18. C. Prieur, J. Winkin and G. Bastin, Robust boundary control of systems of conservation laws. Math. Control Signals Syst. 20 (2008) 173–197. [CrossRef] [Google Scholar]
  19. T.H. Qin, Global smooth solutions of dissipative boundary value problems for first order quasilinear hyperbolic systems. Chinese Ann. Math. Ser. B 6 (1985) 289–298. [Google Scholar]
  20. R. Vazquez, J.-M. Coron, M. Krstic and G. Bastin, Local exponential H2 stabilization of a 2 × 2 quasilinear hyperbolic system using backstepping, in 50th IEEE Conference on Decision and Control and European Control Conference, Orlando (2011) 1329–1334. [CrossRef] [Google Scholar]
  21. R. Vazquez, M. Krstic and J.-M. Coron, Backstepping boundary stabilization and state estimation of a 2 × 2 linear hyperbolic system, in 50th IEEE Conference on Decision and Control and European Control Conference, Orlando (2011) 4937–4942. [CrossRef] [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.