High-performance vehicles use active differentials (AD) to maximize traction, stability, and safety by optimizing the torque distribution on the driving vehicle wheels. This work presents the torque distribution and speeds which are theoretically analyzed using mathematical models of the vehicle, driver, tire and drive train with an AD including the electromechanical actuation. The proposed controller is investigated using MATLAB/Simulink with AD as an external torque by an electromechanical actuation in a variety of driving scenarios, including straight lines under NEDC and J-turn input test with different road adhesions, to regulate lateral slide slip and vehicle yaw rate (YR) on different road adhesions can be obtained by an LQR controller. The results show that the AD can enhance the overall performance of the vehicle dynamics properties by transferring torque between the right and left wheels, which produces the direct yaw moment. The AD with integrated YR and vehicle side slip (VSS) control effectively improves vehicle dynamics and stability under different road maneuvers and adhesions.