A new design method of a stable dynamic output feedback (DOF) controller in linear MIMO systems is presented on the frame of real Grassmann spaces. For the analysis, the DOF systems are decomposed into augmented static output feedback (SOF) systems using signal flow graph analysis of all DOF loops. For synthesis and design, the characteristic polynomial of the augmented SOF system for the system's stable poles and the sub-characteristic polynomial of the sub-SOF system for the controller's stable poles are parametrized within their Grassmann invariants in real Grassmann spaces, whose coordinates are defined in the real coefficient function spaces of their augmented SOF variables. The numerical parametrization and computation algorithm for a stable controller design is illustrated over a MIMO plant of a practical aircraft carrier model.