Robust boundary control of systems of conservation laws

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 cr...

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Bibliographic Details
Published inMathematics of control, signals, and systems Vol. 20; no. 2; pp. 173 - 197
Main Authors Prieur, Christophe, Winkin, Joseph, Bastin, Georges
Format Journal Article
LanguageEnglish
Published London Springer-Verlag 01.06.2008
Springer Nature B.V
Subjects
Boundary conditions
Communications Engineering
Conservation laws
Control
Control systems
Criteria
Friction
Mathematics
Mathematics and Statistics
Mechanical engineering
Mechatronics
Networks
Original Article
Partial differential equations
Robotics
Supplies
Systems Theory
Water
Water shortages
Conservation laws
Robust stability
Hydraulic applications
Nonlinear PDE
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Summary: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.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0932-4194
1435-568X
DOI:10.1007/s00498-008-0028-x