  In this paper, we study the effect of non-vanishing disturbances on the
stability of fixed-time stable (FxTS) systems. We present a new result on FxTS,
which allows a positive term in the time derivative of the Lyapunov function
with the aim to model bounded, non-vanishing disturbances in the system
dynamics. We characterize the neighborhood to which the system trajectories
converge, as well the time of convergence to this neighborhood, in terms of the
positive and negative terms that appear in the time derivative of the Lyapunov
function. Then, we use the new FxTS result and formulate a quadratic program
(QP) that yields control inputs which drive the trajectories of a class of
nonlinear, control-affine systems to a goal set in the presence of control
input constraints and non-vanishing, bounded disturbances in the system
dynamics. We consider an overtaking problem on a highway as a case study, and
discuss how to setup the QP for the considered problem, and how to make a
decision on when to start the overtake maneuver, in the presence of sensing
errors.
