Classical solutions and feedback stabilization for the gas flow in a sequence of pipes

Abstract

We consider the subcritical flow in gas networks consisting of afinite linear sequence of pipes coupled by compressor stations. Suchnetworks are important for the transportation of natural gas overlarge distances to ensure sustained gas supply. We analyse thesystem dynamics in terms of Riemann invariants and study stationarysolutions as well as classical non-stationary solutions for a givenfinite time interval. Furthermore, we construct feedback laws tostabilize the system locally around a given stationary state. To doso we use a Lyapunov function and prove exponential decay withrespect to the $L^2$-norm.