This paper shows the design of a fuzzy attitude control for a spacecraft by using FIS-BBR. The proposed controller guarantees stability in the desired state. Also, it is robust in the presence of uncertainty in the model, external perturbations and noise measurement. In addition, a complete linguistic understanding of the structure of the controller is achieved. The control design process is made by using the knowledge about rotations in three dimensions and a compact genetic algorithm. A method to calculate the Jacobian of the system, including the fuzzy control, is proposed. The Jacobian is used to analyze the system stability.