Lyapunov-based Model for Modern Stabilization Systems of All-wheel Drive Vehicles

Zhilejkin, Mikhail M.
Kozelkov, Oleg A.
Neverov, Vsevolod A.

Automotive Experiences
Vol. 9 No. 1 (2026): Issue in Progress

The study develops a mathematical model of vehicle stability with torque redistribution, aimed at ensuring guaranteed stabilization under non-stationary conditions. Unlike existing methods, the approach combines Lyapunov functions with bifurcation analysis to derive analytical stability criteria for vehicles with mechanical differentials and enables the synthesis of adaptive control strategies that integrate differential locking, wheel braking, and dynamic torque redistribution with formal stability guarantees. The model provides accurate calculations of torque redistribution to the inner or outer wheels during vehicle oversteer or understeer, respectively, ensuring motion stabilization and preserves stability even under sharp steering inputs, as confirmed by phase portraits and transient response analyses. The proposed model was implemented and verified. The model can be incorporated into active safety systems of wheeled vehicles to enhance stability on complex surfaces, reduce computational requirements, and ensure compatibility with existing mechanical drivetrains.