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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 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 $ku003e0$. We show that as long as the $H^1$-norm of the function that describes the noise in the customeru0027s 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 t...

Boundary Feedback Stabilization of the Isothermal Euler Equations with Uncertain Boundary Data