Spacecraft in space may have some certain non-cooperative characteristics due to the service life limit, fuel exhaustion, component fault, structural fatigue damage, or after performing certain space tasks such as capturing non-cooperative targets. In modeling, these non-cooperative characteristics are often manifested in uncertain and unknown inertia, model parameters uncertainty, actuator faults, etc. In this paper, aiming at the attitude stability control problem of such flexible spacecraft, the attitude dynamics modeling is completed by introducing the nominal inertia to construct the comprehensive disturbance term including external disturbance, inertia uncertainty and actuator failure. Then, a static output feedback (SOF) controller is applied to model the closed-loop attitude control system a stable negative imaginary (NI) system with H∞ performance constraints according to NI theory. As long as the optimization variables approach zero, the LMI-based iterative algorithm can find such the static output feedback controller to stabilize the flexible spacecraft. It is worth mentioning that an event-trigger mechanism is introduced into the control scheme to reduce communication pressure. Finally, the numerical simulation is carried out in the presence of controller gain perturbations and model parameter uncertainty. The results of the simulation demonstrate the effectiveness, robustness and non-fragility of the control method.