This paper proposes a complete robust control design procedure for combustion systems, present in a wide range of important applications. Using a non-linear model identified through optical instrumentation, it is proposed a linear model around an operating condition. To ensure robustness with respect to variations on the operation condition and to deal with external disturbances, a state-space linear representation is further developed, introducing uncertain parameters and exogenous inputs affecting the plant (as non-laminar air flow), giving rise to a polytopic uncertain linear system. Finally, it is proposed a reduced-order H-infinity output-feedback control law for the resulting uncertain system, capable to assure closed-loop robust stability and performance in the whole uncertain domain A numerical experiment is presented to show the effectiveness of the designed reduced-order controller, that is robust against uncertainties and have a low cost of implementation. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.