Recently developed results for direct adaptive control design in the context of uncertain systems in de-scriptor form are discussed and applied to a satellite attitude control problem. Thanks to descriptor model handling the methodology allows to address with convexity arguments uncertainties on the inertia matrix. The design of the adaptive law is done with semi-definite programming tools (LMI solvers) and is applicable with the sole knowledge of a controller stabilizing the nominal system (no passivity assumptions). The tackled satellite model is linear (assuming small pointing errors), full 3D rotations are considered (axes are coupled), and mixed reaction wheel and magnetotorquer actuation is adopted. Compared to the provided initial LTI control law, adaptive control increases robustness margins by a factor 262%.