This work deals with the analysis and the design of
minimum-time control laws for a class of nonlinear discrete-time
dynamical systems characterized by -continuous transitionmaps
and bounded control inputs. In the paper, it is shown that the reachability
properties of the target set, even if not robust positively controllable
in one state transition, can be exploited to assess the existence
of a robust positively controllable set including the target in
its interior. This result allows the formulation of a robustified minimum-
time control policy, based on iterated online optimizations
and guaranteeing the ultimate boundedness of the state-trajectories
in the presence of bounded uncertainties, even if the target set
is not robust positively controllable.
