A Rigorous Proof for the Tending-to-One Theorem on Parameter Sum of the Discretized Model of A Continuous-Time System

It is rigorously proved in the paper that,based on the practical condition in computer control,the parameter sum of the discretized model,obtained from a continuous--time linear dynamic system,tends to one with the sampling period approaching zero.This tending--to--one theorem is also extended to a prediction model of the system.The theorem has been proved to be very useful in estimating the all model parameters of a controlled plant in a closed loop via least squares method.