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

  • Martin Gugat
  • Markus Dick
  • Günter Leugering
Part of the IFIP Advances in Information and Communication Technology book series (IFIPAICT, volume 391)

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 C 1-functions with bounded derivatives. In order to analyze the system evolution, we introduce an L 2-Lyapunov function with delay terms. The boundary controls guarantee the exponential decay of the Lyapunov function with time.

Keywords

boundary feedback stabilization Euler equations gas network Lyapunov function star-shaped network time-varying delay 

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Copyright information

© IFIP International Federation for Information Processing 2013

Authors and Affiliations

  • Martin Gugat
    • 1
  • Markus Dick
    • 1
  • Günter Leugering
    • 1
  1. 1.Lehrstuhl 2 für Angewandte MathematikFriedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany

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