  The problem of state-feedback stabilizability of discrete-time nonlinear
systems has been considered in this note. Two assertions have been proved.
First, if the system is $N$-step controllable to the origin, then there is a
state feedback control law for which the trajectory of the closed-loop system
converges to the origin in $N$ steps. Second, if the system is asymptotically
controllable to the origin and satisfies the controllability rank condition at
the origin, then there is a state feedback control law for which the trajectory
of the closed-loop system converges to the origin in finite steps.
