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Robust boundary control of systems of conservation laws

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Abstract

The stability problem of a system of conservation laws perturbed by non-homogeneous terms is investigated. These non-homogeneous terms are assumed to have a small C 1-norm. By a Riemann coordinates approach a sufficient stability criterion is established in terms of the boundary conditions. This criterion can be interpreted as a robust stabilization condition by means of a boundary control, for systems of conservation laws subject to external disturbances. This stability result is then applied to the problem of the regulation of the water level and the flow rate in an open channel. The flow in the channel is described by the Saint-Venant equations perturbed by small non-homogeneous terms that account for the friction effects as well as external water supplies or withdrawals.

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Authors and Affiliations

  1. LAAS-CNRS, Université de Toulouse, 7, avenue du Colonel Roche, 31077, Toulouse, France

    Christophe Prieur

  2. Department of Mathematics, University of Namur (FUNDP), 8, Rempart de la Vierge, 5000, Namur, Belgium

    Joseph Winkin

  3. CESAME, Catholic University of Louvain, 1348, Louvain-la-Neuve, Belgium

    Georges Bastin

Authors
  1. Christophe Prieur
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  2. Joseph Winkin
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  3. Georges Bastin
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Correspondence to Christophe Prieur.

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Prieur, C., Winkin, J. & Bastin, G. Robust boundary control of systems of conservation laws. Math. Control Signals Syst. 20, 173–197 (2008). https://doi.org/10.1007/s00498-008-0028-x

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  • DOI: https://doi.org/10.1007/s00498-008-0028-x

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