Lyapunov stability of the roll-yaw and pitch subsystems of a linearized spacecraft attitude control system are re-examined, along the lines of a previously proposed Jordan form-based approach. It is found that the roll-yaw subsystem is Lyapunov stable for inertially symmetric spacecraft with repeated eigenvalues on the imaginary axis, which cannot be asserted by the existing characteristic equation based approach. Globally stabilizing controllers with bounded linear feedback are then designed for such spacecraft and the optimal feedback gain is designed such that the convergence rate of the linearized dosed-loop system is maximized. The proposed method is also applicable to inertially symmetric spacecraft with magnetic actuators. (C) 2019 Elsevier Ltd. All rights reserved.