Existence of classical solutions and feedback stabilization for the flow in gas networks
Lehrstuhl 2 für Angewandte Mathematik, Martensstr. 3, 91058 Erlangen,
2 RWTH Aachen, Lehrstuhl C für Mathematik, Templergraben 55, 52065 Aachen, Germany. firstname.lastname@example.org
Revised: 11 June 2009
We consider the flow of gas through pipelines controlled by a compressor station. Under a subsonic flow assumption we prove the existence of 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 compressor station. We introduce a Lyapunov function and prove exponential decay with respect to the L2-norm.
Mathematics Subject Classification: 76N25 / 35L50 / 93C20
Key words: Classical solution / networked hyperbolic systems / gas networks / feedback law / Lyapunov function
© EDP Sciences, SMAI, 2009