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 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.