Brief paper: Lyapunov exponential stability of 1-D linear hyperbolic systems of balance laws

Authors:
Ababacar Diagne;Georges Bastin;Jean-Michel Coron
Affiliations:
UFR de Sciences Appliquées et Technologies, Université Gaston Berger, BP 234, Saint-Louis, Sénégal;Department of Mathematical Engineering, Université catholique de Louvain, 4, Avenue G. Lemaitre, 1348 Louvain-La-Neuve, Belgium;Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Institut Universitaire de France, 4, Place Jussieu, 75252 Paris Cedex, France
Venue:
Automatica (Journal of IFAC)
Year:
2012

Citing 3
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Boundary observers for linear and quasi-linear hyperbolic systems with application to flow control

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Abstract

Explicit boundary dissipative conditions are given for the exponential stability in L^2-norm of one-dimensional linear hyperbolic systems of balance laws @?"t@x+@L@?"x@x-M@x=0 over a finite interval, when the matrix M is marginally diagonally stable. The result is illustrated with an application to boundary feedback stabilisation of open channels represented by linearised Saint-Venant-Exner equations.