Analysis of feedback control scheme on discrete car-following system

We discretized the Newell's car-following model into a difference equation and the impulse transfer function is derived. The stability condition is given and proven as a Lemma based on bilinear transformation and Routh criteria. Feedback control scheme was applied to improve the performance of car-following system. A theorem was proposed to judge the stability condition in designing the feedback coefficient for controlled car-following system. Numerical simulations were conducted to verify the validity of the discrete car-following model and its control scheme. The simulation results show that the sampling time and feedback control coefficient have effects on the stability of car-following system.