This paper considers a single-input, linear, time-invariant, sampled-data system described by its state transition equation xk+1 = Axk + fk+la, where the control fk+1 is subject to the admissibility condition I fk+1 |1. Necessary and sufficient conditions for controllability with admissible controls are derived. For any system satisfying these conditions, the following problem is solved: determine a scalar valued function f(x) such that if, at each sampling instant, f(x) is used as a control when the system is at state x at that sampling instant, then, given any initial state x0, the system will be brought to the origin in the minimum number of sampling periods. In other words, f(x) constitutes an optimal strategy for the minimal time regulator problem. The function f(x) is describable as follows: (1) in the state space, a hypersurface is constructed; (2) the line through x1, parallel to r1 = - A−1a intersects at point c, thus x = c + λr1; (3) f(x) = sat λ.