Third-order consensus in vehicles platoon with heterogeneous time-varying delays

We theoretically address the problem of achieving third-order consensus for a platoon of vehicles in the presence of heterogenous time-varying communication delays. A Lyapunov-Krasovkii function is constructed for the stability analysis. Necessary and su?cient conditions are derived to guarantee that all vehicles asymptotically reach the relative acceleration, speed and position according to the spacing policy. Numerical simulations are provided to demonstrate the effectiveness of the theoretical results in different driving conditions and in the presence of external disturbances.