  A major challenge in autonomous driving is designing control architectures
that guarantee safety in all relevant driving scenarios. Given a safe desired
reference trajectory for the vehicle, a trajectory following controller has to
ensure that the trajectory is followed with a maximally allowed deviation, even
in the presence of external disturbances, such as wind gusts or inclined roads.
In this paper, a method for computing upper bounds for linear, time invariant
single-input-multiple-output systems with state feedback controllers and
additive bounded disturbances is proposed. The bounds for the offset between
states and the reference are derived analytically based on worst case
disturbance sequences. For systems with two states the bounds are strict, while
for higher order systems they are conservative. The method is applied to obtain
position bounds for lateral trajectory following controllers, and to analyze
how different choices of feedback parameters affect safety margins.
