Let n be the dimension of the Brunovsky system. For n = 2m (respectively n = 2m + 1), we prove that every positive distribution on [0, ∞) that has at least n/2 points of increase on (0, ∞), (respectively (n + 1)/2 points of increase on [0, ∞) generates a positional control that stabilizes a family of Brunovsky systems of dimensions 1 ≤ k ≤ n.