Abstract
This paper deals with the relation between a sampling period T and the set of all initial states which are to be forced to the origin in less than m iterations with the period T by the admissible control. The set is called a controllable set and denoted by C(T, m). First, the author obtains some properties of the set C(T, m) for the 2nd-order single-input systems. And these results are extended to the nth-order r-input systems. Especially it is shown that the period p such that C(T, m)⊂C(p, m) is given by the equation p≥mT/(m-1) under some conditions irrespective of the system class.
