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. And the input penalty factor of the adaptive cruise control system is designed as a variable parameter for the collaborative control model. On this basis, the longitudinal speed, reciprocal of speed and penalty factor are used as advance variables to design fuzzy rules of the system. And the nonlinear Takagi-Sugeno fuzzy model is established by fuzzifying the local linear model. Then, the vehicle following cruise controller considering the lateral stability is designed by parallel distribution compensation method. Finally, the TruckSim/Simulink co-simulation model was built for testing. The test results show that the proposed controller can improve the lateral stability of the vehicle during the following process, reduce the risk of instability of the vehicle, and improve the overall safety of the automatic driving system.