  In a gas transport system, the customer behavior is uncertain. Motivated by
this situation, we consider a boundary stabilization problem for the flow
through a gas pipeline, where the outflow at one end of the pipe that is
governed by the customer's behavior is uncertain. The control action is located
at the other end of the pipe. The feedback law is a classical Neumann velocity
feedback with a feedback parameter $k>0$.
  We show that as long as the $H^1$-norm of the function that describes the
noise in the customer's behavior decays exponentially with a rate that is
sufficiently large, the velocity of the gas can be stabilized exponentially
fast in the sense that a suitably chosen Lyapunov function decays
exponentially. For the exponential stability it is sufficient that the feedback
parameter $k$ is sufficiently large and the stationary state to which the
system is stabilized is sufficiently small. The stability result is local, that
is it holds for initial states that are sufficiently close to the stationary
state.
  This result is an example for the exponential boundary feedback stabilization
of a quasilinear hyperbolic system with uncertain boundary data. The analysis
is based upon the choice of a suitably Lyapunov function. The decay of this
Lyapunov function implies that also the $L^2$-norm of the difference of the
system state and the stationary state decays exponentially.
