  Autonomous vehicle following systems are playing a decisive role to increase
vehicle density on roads by shortening inter-vehicle time gaps. However,
disturbance attenuation along a platoon of vehicles, i.e., string stability, is
being a challenging task while time gap is getting shorter. In order to
guarantee the string stability of a vehicle platoon, a multi-objective
$H_{\infty}$ control formulation for adaptive cruise control and cooperative
adaptive cruise control structures has been investigated in this paper. The
proposed control method solves an optimization problem and achieves a
controller that is able to provide not only the system stability, but also the
string stability as distinct from the traditional $H_{\infty}$ control.
