This paper investigates the control of laminar combustion processes represented by a class of one–dimensional, non-linear, reaction–diffusion equations. The control objective is to regulate the spatial location of a propagating flame front dynamically by varying the fuel-air velocity. It is shown that when viewed from an input–output perspective, the problem is equivalent to the control of a system consisting of linear elements and a single time-varying non–linear element. The system is controlled using a linear compensator that is designed based on an H∞(minimax) optimality criterion.