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 kT , the input is u_{k}f(t - kT) , where u k is a real constant and f(t) is a bounded piecewise continuous shaping-function given in 0 . Necessary and sufficient conditions for complete controllability of such sampled-data systems in terms of T and f(t) are given. This is a generalization of a well-known theorem for the special case f(t) \equiv 1 due to Kalman et al. The results may prove to be important if for practical reasons the shaping function f(t) \equiv 1 cannot be realized.