Abstract
In this paper we study questions regarding controllability of a distributed parameter system in the case of discrete-time controls. We present the necessary and sufficient conditions for controllability. For the systems with finite-dimensional control functions, we also investigate the relations between a discrete-time control system and a continuous-time control system from the controllability point of view. We show that the distributed systems will never be N-step controllable for any finite N. Moreover we give the set whose elements are attainable by means of N-step controls.
