Plasma density control for next generation tokamaks, such as ITER, is challenging because of multiple reasons. The response of the usual gas valve actuators in future, larger fusion devices, might be too slow for feedback control. Both pellet fuelling and the use of feedforward-based control may help to solve this problem. Also, tight density limits arise during ramp-up, due to operational limits related to divertor detachment and radiative collapses. As the number of shots available for controller tuning will be limited in ITER, in this paper, iterative learning control (ILC) is proposed to determine optimal feedforward actuator inputs based on tracking errors, obtained in previous shots. This control method can take the actuator and density limits into account and can deal with large actuator delays. However, a purely feedforward-based density control may not be sufficient due to the presence of disturbances and shot-to-shot differences. Therefore, robust control synthesis is used to construct a robustly stabilizing feedback controller. In simulations, it is shown that this combined controller strategy is able to achieve good tracking performance in the presence of shot-to-shot differences, tight constraints, and model mismatches.