  The flow of gas through networks of pipes can be modeled by coupling
hyperbolic systems of partial differential equations that describe the flow
through the pipes that form the edges of the graph of the network by algebraic
node conditions that model the flow through the vertices of the graph. In the
network, measurements of the state are available at certain points in space.
Based upon these nodal observations, the complete system state can be
approximated using an observer system. In this paper we present a nodal
observer, and prove that the state of the observer system converges to the
original state exponentially fast. Numerical experiments confirm the
theoretical findings.
