Simple algebraic structure of Taylor expansion of sampled-data systems

The relation between the continuous-time model and the corresponding discrete-time model of sampled-data system has not been believed to be very simple. However, from the view point of Taylor expansion with respect to sample time, the relation is approximated by unexpectedly simple polynomials. In this paper, we show that there is a simple regularity in Taylor expansion for any sampled-data systems. Next, it is demonstrated that the regularity reduces symbolic calculation of the Taylor expansion. Finally, we apply the result to identification of continuous-time model from discrete-time input-output data of sampled-data systems based on optimization techniques.