String Stability of a PI-controlled Vehicular Platoon

This paper studies the asymptotic stability and string stability conditions for platoons composed of vehicles modelled by single integrator dynamics that are locally controlled by PI controllers with a constant time-headway spacing policy. The novelty of the work lies on not considering that the controller dynamics cancel the ones introduced by the spacing policy, which is a common strategy to simplify the analysis. In this setup, we obtain conditions for string stability that reveal two zones in the space spanned by the design parameters of the platoon that are compatible with this property. We also provide numerical simulations that verify the derived conditions.