Abstract: The paper considered the output feedback disturbance rejection problem based on internal-model principle for linear systems.According to the disturbance dynamics,the internal model was constructed.The optimal disturbance rejection problem was transformed into an equivalent optimal regulation problem for the augmented system.Then,a reduced-order state observer was constructed to reconstruct the unmeasurable state variables from the output feedback.The suboptimal control law was derived from series matrix differential equations or matrix equations,in which the disturbance was eliminated by the internal-model compensator.Finally,a simplified offshore platform system was applied for simulation example.Comparing with the feedforward and feedback optimal disturbance rejection control law,the designed controller was validated to be able to reject disturbance without steady-state error.