With the increasing demands for the agility of the next earth imaging satellite, control moment gyro (CMG) is considered to be the most suitable actuator because of its torque amplification capability. However, a CMG system may introduce uncertainty of inertia dyadic to a satellite's attitude control system. The uncertainty is negligible for large space vehicles, but it has not been tested whether it can be ignored for small agile satellites. How to model the CMG system inertia dyadic varying with gimbal angles, and what influence it will put on the performance of attitude control system haven't been test accurately as well. All of them are dealt with mathematically and accurately in this paper. This paper firstly gives mathematic descriptions of the inertia dyadic of the 4-CMG pyramid configuration system, varying with gimbal angles, and then designs a variable structure control law for small agile satellite using CMGs. Finally, numerical simulation suggests that the inertia dyadic variation of a 4-CMG pyramid configuration system is approximately centesimal of the total inertia dyadic of the satellite, and that the designed variable structure control law is of good robust performance for an example of large-angle attitude maneuver, despite of the variation of the inertia dyadic.
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