Stability analysis of a longitudinal control law for autonomous vehicles

We focus on the analysis of an acceleration law for a following autonomous vehicle with constant time headway goal. We first define a function that measures the positioning of the following vehicle compared to the leading vehicle, with respect to the desired time headway. We study the convergence and limit of this positioning function, and prove the asymptotic stability of our acceleration control law under some initial conditions on the following vehicle and some invariant conditions on the leading vehicle. We then extend this result when the acceleration are saturated by the technology bounds, and we apply it to prove the platoon stability. Finally, we conduct several simulations that validate our theoretical results and show the impact of the initial conditions