The objective of this internship is the design of different control strategies for the primary frequency control of a microgrid composed of a diesel generator, a photovoltaic source, an energy storage system and a load. Dynamic modelling in the form of state-space representation oriented to the control design is carried out. Firstly, a classical control approach is proposed as a reference. Then, a robust control synthesis based on an optimal linear multi-variable control theory and a so-called H∞ mixed sensibility optimisation, is applied to the studied hybrid system. The idea is, in the first time, to synthesize this control by ensuring a certain number of performance during the disturbance on the system. In the second step, several modelling uncertainties are included and μ-analysis is implemented to determine the maximum variation range of each uncertainty while ensuring system stability on the one hand, and desired performance on the other hand. Then, the advantage of the multi-variable approach over the classical decoupled control methodology is studied. Finally, this report ends with conclusions and perspectives.