This paper discussed the optimal feedback stabilization problem of a yaw-pitch gimbaled system with structure uncertainties, actuator saturation and disturbance torques in its control channels. The influence modes of platform angular motion, kinematics & geometrical coupling and unbalance moments on system dynamics were analyzed from the perspective of gimbal dynamics. Optimal feedback controllers were synthesized by means of Linear Matrix Inequalities (LMIs) and convex optimization to prevent the system from the instability caused by disturbance torques and actuator saturation. Simulation results prove the robustness of the derived optimal feedback controllers against system uncertainties, actuator saturation and disturbance torques.