Car accidents caused by driver's fatigue, inattention, drowsiness and illness are one of the leading reasons for preventable fatalities and injuries on the road. This paper studies the assistant driving problem for the nonlinear lateral dynamic model of vehicles in the lane keeping case. By means of the developed controller the car is able to keep itself in a given lane even if the human driver does not drive properly. The shared-control algorithm is based on a hysteresis switch and the formal properties of the closed-loop system are established via a Lyapunov-like analysis. Simulation results are presented to show the effectiveness of the driving assistant system.