In this paper we examine the ability of H∞-control theory to perform actually linear control of distributed parameter systems in non-trivial cases. The process to be controlled is originally an alumina furnace, which is modelled by trivializing combustion phenomena as a rather special heat exchanger. This process has an intrinsic non-minimum phase, due to its particular geometry. It is modelled as a non-linear partial differential system, which is linearized and controlled using H∞-techniques. Algorithms are developed to accomplish this task, in particular to factorize the (transcendental) transfer function into its inner and outer parts. Simulation and comparisons with classical controllers are performed