In this work, we propose an uncertainty-aware controller for the Fly-Crane system, a statically rigid cable-suspended aerial manipulator using the minimum number of aerial robots and cables. The force closure property of the Fly- Crane makes it ideal for applications where high precision is required and external disturbances should be compensated. The proposed control requires the knowledge of the nominal values of a minimum number of uncertain kinematic parameters, thus simplifying the identification process and the controller implementation. We propose an optimization-based tuning method of the control gains that ensures stability despite parameter uncertainty and maximizes the H∞ performance. The validity of the proposed framework is shown through real experiments.