<p>Trajectory tracking control on slippery roads presents significant challenges for autonomous vehicles due to nonlinear tire dynamics and reduced road adhesion. This paper proposes a trajectory tracking control framework based on a stability margin approach to improve both tracking accuracy and stability in such conditions. First, by analyzing the front and rear tire slip angles in the phase plane, we identify critical saddle points and define a stability boundary for tire slip angles. A corresponding stability index is formulated to quantify how close the vehicle is to its handling limits, enabling the control strategy to dynamically balance maneuverability and stability. This stability index is then integrated into a model predictive controller (MPC), allowing adaptive weight adjustments to prioritize either precise trajectory tracking or enhanced stability. Hardware-in-the-loop (HIL) experiments demonstrate that the proposed method can effectively improve the path tracking accuracy and ensure the handling stability. Compared with the conventional MPC strategy, the adaptive MPC reduces the longitudinal speed root mean square error (RMSE) by 65.10% and 9.38% on variable speed double lane change maneuver and split friction double lane change maneuver, the RMSE values of yaw rate and sideslip angle decreased by 33.96% and 24.00%, respectively. The results indicate its potential for real-time deployment in autonomous vehicles tracking slippery conditions.</p>