[Purposes] Aiming at the multi-objective control of vehicle lateral stability and tracking accuracy in the process of vehicle trajectory tracking, a cooperative control strategy of vehicle trajectory tracking and lateral stability based on extension set is proposed taking. [Methods] A unified vehicle model including vehicle trajectory tracking accuracy and lateral stability was established， the upper controller was realized based on sliding mode control strategy, and the steering angle for vehicle trajectory tracking and the direct yaw moment to improve lateral stability were planned. Combined with the extension set theory, an adaptive adjustment method of two control weights of trajectory tracking accuracy and lateral stability was proposed to realize the collaborative control of two control objectives. Taking advantage of the independent control of four wheel torques for distributed drive electric vehicle, a wheel torque distribution control strategy to maximize the utilization of road adhesion limit was proposed to achieve the purpose of reliable realization of direct yaw moment. [Findings] Applying the co-simulation of MATLAB/Simulink and CarSim, the proposed cooperative control strategy improves the vehicle lateral stability while ensuring the trajectory tracking accurate. [Conclusions] The simulation results show that the extension distance based on the vehicle lateral stability index can accurately evaluate the vehicle lateral stability, the proposed adaptive adjustment method of control weights can coordinate the trajectory tracking accuracy and lateral stability, and the torque distribution control strategy can reliably realize the direct yaw moment.