Hydrogen fuel cells are a promising option to provide renewable and clean energy to various mobile applications and aviation, as one of the most demanding engineering fields, requires a minimalist integration of the fuel cells into the onboard power systems to reduce the overall weight. Therefore, a direct coupling between fuel cell and the electric motor without a DC/DC converter, or a sophisticated inverter, but rather just a high-speed switch (e.g. MOSFET), could reduce the system weight significantly. Such an implementation would expose the fuel cell to significant load fluctuations (on-off current ripple), which can adversely affect the longevity of the fuel cell. The integration of an electric field modifier (EFM) electrode as an additional control input in order to stabilise the resulting high frequency oscillations is investigated, and the required controller is designed. An EFM was introduced elsewhere as a high surface area metal mesh electrode integrated into the membrane of the fuel cell. This creates an additional high capacitance double layer capacitor within the fuel cell system, which can be used to affect high frequency small signal perturbations, such as the voltage fluctuations due to a high frequency current ripple. Using experimental data from polarisation curve and electrochemical impedance spectroscopy measurements on a single cell, an equivalent circuit model of the fuel cell is derived. The model is linearised for a medium current level of 6 A with a DC contribution of 1 A representing the power requirements of ancillary devices in the onboard power system. A 20 kHz square wave with ±5 A amplitude will be used as the design point for the controller. Starting from this linearised model of the fuel cell, the optimal H∞-controller is designed and tested. The optimal H∞-controller already stabilised the voltage to less than ±5 mV. In the next step a feedforward component is added to the control system in order to improve the stabilisation of the fuel cell voltage even further. For the linearised model this control system is able to stabilise the resulting voltage to within ±10 µV. The full control system is then applied to a simulated load profile of a flight (taxiing, take-off, climb, cruise, descent), using a second version of the equivalent circuit model accounting for the nonlinear behaviour of both the anode and cathode reaction. Therefore, the model for the system more closely reflects the overall operational range. Compared to the original system without a controller, the resulting voltage fluctuations can already be significantly reduced by just using the optimal H∞-controller, however, when combined with the feedforward component, the voltage of the fuel cell can be stabilised to less than ±3 mV with respect to the corresponding average voltage of the quasi-stationary operating point in the operational range. This will improve the longevity of the fuel cell in the long run. For a physical application of the idea, the next step would be a discretised model and controller design using a sampling time, which could realistically be achieved with a control system, since both model and disturbance are very fast reacting systems.