  This paper proposes a vehicular platoon control approach under
Denial-of-Service (DoS) attacks and external disturbances. DoS attacks increase
the service time on the communication network and cause additional transmission
delays, which consequently increase the risk of rear-end collisions of vehicles
in the platoon. To counter DoS attacks, we propose a resilient control scheme
that exploits polytopic overapproximations of the closed-loop dynamics under
DoS attacks. This scheme allows synthesizing robust controllers that guarantee
tracking of both the desired spacing policy and spatially varying reference
velocity for all space-varying DoS attacks satisfying a hard upper bound on the
attack duration. In addition, L2 string stability conditions are derived to
ensure that external perturbations do not grow as they propagate through the
platoon, thus ensuring the string stability. Numerical simulations illustrate
the effectiveness of the proposed control method.
