Time-delayed boundary feedback stabilization of the isothermal Euler equations with friction

Abstract

We consider the isothermal Euler equations with friction that modelthe gas flow through pipes. We present a method of time-delayedboundary feedback stabilization to stabilize the isothermal Eulerequations locally around a given stationary subcritical state on afinite time interval. The considered control system is a quasilinearhyperbolic system with a source term. For this system we introduce aLyapunov function with delay terms and develop time-delayed boundarycontrols for which the Lyapunov function decays exponentially withtime. We present the stabilization method for a single gas pipe andfor a star-shaped network of pipes.