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It is difficult for a conventional robust control algorithm to assure the performance of a slip speed control system, because the plant (lockup system) includes the nonlinear characteristics of the hydraulic system and large changes in the parameters of the slip model at low vehicle speed. The purpose of this study is to reduce the fuel consumption and improve the drivability of vehicles at takeoff by using a slip speed control system. Providing a large feedback gain is effective in reducing the influence of nonlinearity. However, since the operating parameters of the lockup clutch change depending on the driving conditions, that is not possible. A feedback compensator with a gain-scheduled H∞ control method was used in this study to solve these problems. The effectiveness of the slip speed control system was demonstrated in driving tests. Using this control system, the slip speed can be controlled with high accuracy, thereby reducing unnecessary revving of the engine.