Construction crane vessels make use of dynamic positioning (DP) systems during the installation and removal of offshore structures to maintain the vessel's position. Studies have reported cases of instability of DP systems during offshore operation caused by uncertainties, such as mooring forces. DP“robustification” for heavy lift operations, i.e., handling such uncertainties systematically and with stability guarantees, is a long-standing challenge in DP design. A new DP method, composed by an observer and a controller, is proposed to address this challenge, with stability guarantees in the presence of uncertainties. We test the proposed method on an integrated cranevessel simulation environment, where the integration of several subsystems (winch dynamics, crane forces, thruster dynamics, fuel injection system etc.) allow a realistic validation under a wide set of uncertainties.