Global stability of road vehicle motion with driver control

Abstract The paper contributes to unveil how drivers—either human or not—may lose control of road vehicles after a disturbance. First, simple vehicle-and-driver model is considered: Its motion characterized by the existence limit cycles whose amplitude depend on vehicle forward velocity (both oversteering and understeering may exibit this property). Such are originated Hopf bifurcation occurring at relatively high velocity. A mathematical proof bifurcations given. saddle confirmed experimental tests performed dynamic driving simulator with complex in loop. By Zubov method, Lyapunov function derived compute region asymptotic stability for model. necessary sufficient condition global stability. refers variation kinetic energy which must vanish end disturbed motion. This occurrence has been detected too. Just single stable equilibrium found inside domain attraction all examined cases.