A series of discrete-time models of a continuous-time system based on fluency signal approximation

A series of discrete-time models of a continuous-time system based on m-order fluency signal approximation is derived. It is shown that the series of models includes and generalizes the conventional system model based on the assumption of staircase (sample hold) signal input (m = 1). The adaptive discretization is obtained by selecting the appropriate order m within a given tolerance of the approximation error incurred in assuming the input signal according to the characteristics (continuous differentiability) of input signals of the continuous-time system dealt with