Certain combustion processes are inherently unstable due to the coupling of the flame and the acoustic modes of the combustion chamber. Such instabilities lead to oscillating heat release and pressure, which are undesirable. A means to eliminate these oscillations is to design a controller to monitor the fluctuating pressure upstream and modulate the fuel injection accordingly. Making use of a recently developed nonlinear model for a premixed ducted flame, we demonstrate in this paper advances in robust control can be used to methodically synthesize a controller and analyse the resulting closed-loop system. Precisely, H-infinity loop-shaping is employed to obtain a controller and mu-analysis and Integral Quadratic Constraints are applied to prove the closed-loop stability of the nonlinear model. Open-and closed-loop simulations are also provided.