Aiming at the economy and security of the positioning system in semi-submersible platform, the paper presents a new scheme based on the mooring line switching strategy. Considering the input delay in switching process, control with time-varying input delay is designed to calculate the control forces to resist disturbing forces. In order to reduce the conservativeness, the information of the lower bound of delay is taken into account, and a Lyapunov function which contains the range of delay is constructed. Besides, the input constraint is considered to avoid breakage of mooring lines. The sufficient conditions for delay-range-dependent stabilization are derived in terms of LMI, and the controller is also obtained. The effectiveness of the proposed approach is illustrated by a realistic design example. 1. Introduction For oil and gas exploration in waters deeper than 300 meters, floating platforms such as drillship and semisubmersible platforms are used. These platforms must be kept at a desired location accurately to accomplish the exploration tasks, so it is important to design appropriate positioning system. Dynamic positioning (DP) and mooring positioning system have been used for many years [1]. S？rensen et al. researched the thruster-assisted position mooring (PM) based on DP [2, 3]. The mooring system provides effectively passive control in moderate weather conditions, while the thruster can perform active control to assist the mooring system in severe environmental conditions. So, PM is often considered to be the most cost-effective and feasible positioning method. However, PM also has some shortcomings. Compared with mooring system, although the positioning precision is improved, the cost of initial construction, usage, and maintenance is increased. Compared with DP system, the maneuverability is decreased. So, the first motivation of this paper is to propose a new positioning scheme, which not only improves the positioning precision, but also needs no extra hardware devices in order to ensure economy. Compared with the conventional mooring system, the new scheme adds active mooring line release control to improve the positioning accuracy and uses four three-sprocket windlasses instead of twelve single-sprocket windlasses to control twelve mooring lines release based on mooring line switching. Because windlasses are the intrinsic devices in mooring system, compared with PM, the new scheme saves the thruster installation and maintenance cost; besides, fewer windlasses are adopted, so the total cost of the positioning system is reduced and the
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