The offshore wind market is growing, resulting in larger wind turbines being installed farther away from the coast and into deeper waters. This trend brings challenges to an industry strongly depending on the use of jack-up vessels. A floating vessel equipped with a Dynamic Positioning (DP) system and a Motion Compensated Gripper Frame (MCGF) provides a more efficient solution to guide XXL monopoles during the installation phase. According to strict regulations, the offset angle of monopiles shall not be over 0.25°. To ensure this, a robust control method is required to deal with gradual change in soil stifness, wave induced motions and sensor delays. The control force exerted by the gripper frame can significantly affect the floating vessel dynamics, hence, this should be optimized. Therefore, the research goal is to analyse the system and design a robustly stable control for the MCGF. In the context of this research, cascade PID control with gain-scheduling is chosen, which is able to control the Gripper Frame during all installation steps for different soil stiffness and to reject wave disturbances. With the use of the lumped multiplicative uncertainty structure, the changing and uncertain soil-characteristics are modelled. The sensor delay to measure the monopile inclination, has a significant impact on system stability. Robust stability criteria are validated using the Nyquist criterion and by analysing the system's closed-loop poles. With the use of gain-scheduling it is possible to switch control settings during the installation. Time-domain results show that with this design approach the installation criteria are met such as the maximum monopile angle and the applied control force. Ultimately, it is shown that robust PID control with gain-scheduling for a MCGF can ensure safe, efficient and cost-effective installation of the next generation wind turbines. Future research should focus into the definition and implementation of the gain-scheduling switching criteria.