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Stabilization of the Gas Flow in Star-Shaped Networks by Feedback Controls with Varying Delay

Abstract : We consider the subcritical gas flow through star-shaped pipe networks. The gas flow is modeled by the isothermal Euler equations with friction. We stabilize the isothermal Euler equations locally around a given stationary state on a finite time interval. For the stabilization we apply boundary feedback controls with time-varying delays. The delays are given by C1-functions with bounded derivatives. In order to analyze the system evolution, we introduce an L2-Lyapunov function with delay terms. The boundary controls guarantee the exponential decay of the Lyapunov function with time.
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Martin Gugat, Markus Dick, Günter Leugering. Stabilization of the Gas Flow in Star-Shaped Networks by Feedback Controls with Varying Delay. 25th System Modeling and Optimization (CSMO), Sep 2011, Berlin, Germany. pp.255-265, ⟨10.1007/978-3-642-36062-6_26⟩. ⟨hal-01347545⟩

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