LMI-based design of a robust direct adaptive attitude control for a satellite with uncertain parameters*

Three axes attitude control of CNES microsatellite is considered. The satellite has uncertain inertia, natural frequency and damping. Satellite dynamics are modelized using descriptor form, with matrices affinely dependent on the uncertain parameters. LMI-based methods using S-variables allow to design a robust adaptive controller with tunable gain adaptation parameters. Illustrated simulations show that the controller stabilizes the satellite with any inertia physically acceptable. Theoretical results can be applied to any descriptor system rational in the uncertainties.