R-RoMulOC is a freely distributed toolbox aimed at making easily available to the users various optimization-based methods for dealing with uncertain systems. It implements both deterministic LMI-based results, which provide guaranteed performance for all values of the uncertainties, and probabilistic randomization-based approaches, which guarantee performance for all values of the uncertainties except for a subset with arbitrary small probability measure. The paper is devoted to the description of these two approaches for analysis and control design when applied to a satellite benchmark proposed by the CNES, the French Space Agency. The paper also describes the modeling of the DEMETER satellite and its integration into the R-RoMulOC toolbox as a challenging test example. Design of state-feedback controllers and closed-loop performance analysis are carried out with the randomized and robust methods available in the R-RoMulOC toolbox.