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Existence of classical solutions and feedback stabilization for the flow in gas networks

Published online by Cambridge University Press:  11 August 2009

Martin Gugat and
Michaël Herty
Martin Gugat
Affiliation:
Lehrstuhl 2 für Angewandte Mathematik, Martensstr. 3, 91058 Erlangen, Germany. gugat@am.uni-erlangen.de
Michaël Herty
Affiliation:
RWTH Aachen, Lehrstuhl C für Mathematik, Templergraben 55, 52065 Aachen, Germany. herty@mathc.rwth-aachen.de

Abstract

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We consider the flow of gas through pipelines controlled by a compressorstation. Under a subsonic flow assumption we prove the existenceof classical solutions for a given finite time interval.The existence result is used to construct Riemannian feedback laws and to prove a stabilization result for a coupled system of gas pipes with a compressorstation. We introduce a Lyapunov function and prove exponential decay with respect to the L2-norm.

Keywords

Classical solutionnetworked hyperbolic systemsgas networksfeedback lawLyapunov function

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 17 , Issue 1 , January 2011, pp. 28 - 51
Copyright
© EDP Sciences, SMAI, 2009

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