On the first-order and slewer hold equivalent discrete-time models

A definition of discrete-time models with order higher than or equal to that of the continuous-time system is presented. In this definition, a discrete-time model is valid if the outputs of the model and continuous-time system converge in some sense, as the sampling interval approaches zero, provided their inputs also converge. A convenient theorem is derived for relating discrete-time models to their continuous-time counterparts. It is shown that the first-order and slewer hold equivalent models are valid discrete-time models.