This paper presents the design and simulation test of an assistance system that helps the driver to perform vehicle following maneuvers. When activated, the assistance system drives the vehicle to the desired inter-vehicle distance. Based on Lyapunov theory and invariant sets, the assistance system is able to guarantee that the state trajectories remain bounded under bounded disturbance inputs, such as leading vehicle accelerations. The assistance system is designed in such a way that variable time headway strategy is naturally handled. The control law is computed using Linear and Bilinear Matrix Inequalities (LMI-BMI) methods. Some design parameters can be adjusted to handle the tradeoff between safety constraints and comfort specifications.