Controllability of linear time-invariant sampled-data systems with nonconstant shaping functions

This paper is concerned with the controllability of single-input linear time-invariant plants after introduction of sampling in such a way that, for the time , the input is , where ukis a real constant and is a bounded piecewise continuous shaping-function given in . Necessary and sufficient conditions for complete controllability of such sampled-data systems in terms of and are given. This is a generalization of a well-known theorem for the special case due to Kalman et al. The results may prove to be important if for practical reasons the shaping function cannot be realized.