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Adaptive cruise control is one of the key technologies in advanced driver assistance systems. However, improving the performance of autonomous driving systems requires addressing various challenges, such as maintaining the dynamic stability of the vehicle during the cruise process, accurately controlling the distance between the ego vehicle and the preceding vehicle, resisting the effects of nonlinear changes in longitudinal speed on system performance. To overcome these challenges, an adaptive cruise control strategy based on the Takagi-Sugeno fuzzy model with a focus on ensuring vehicle lateral stability is proposed. Firstly, a collaborative control model of adaptive cruise and lateral stability is established with desired acceleration and additional yaw moment as control inputs. Then, considering the effect of the nonlinear change of the longitudinal speed on the performance of the vehicle system.