Stable flow controllers are usually preferred since, compared with unstable flow controllers, they are less sensitive to any modelling imperfections. H-infinity-optimal flow controllers involve finite impulse-response (FIR) filters due to the time delays which are inherent in any practical network. Therefore, design of a stable H-infinity flow controller is a difficult problem due to the infinite dimensionality of these FIR filters. In this work, finite-dimensional approximations of FIR filters are used to design stable H-infinity flow controllers. Three design approaches are considered and, for each approach, a different algorithm to design a stable H-infinity flow controller is developed. Controllers obtained by each agorithm are also compared against each other, as well as against the optimal controller, using an example case.