Erbium-doped fiber amplifiers (EDFAs) form the backbone of high-capacity lightwave communication systems by providing fast optical signal amplification directly on the physical layer. However, current EDFA control schemes lack a systematic approach for design and do not consider the systems' input disturbance characteristics. In this thesis, we propose the application of Hinfinity control for EDFAs subject to two types of known input signal disturbances. Specifically, we propose the use of Hinfinity control to suppress the cross-gain modulation effects of pilot tones used for optical monitoring and packet and burst-switched traffic commonly found in Optical Burst Switched networks. A detailed approach for the Hinfinity controller design is given, focussing on the inherent characteristics of the input disturbances, the optical system itself and desired performance measures. Through the use of MATLAB, simulation results for both types of disturbances are presented showing significant improvements in response time and cross gain modulation suppression.