Parameter Relations between the Linear Continuous Time System Model and Its Sampled Version with Relatively Small Sampling Period

The general relations between the model parameters of a continuous time system and its sampled version are firstly reviewed, and some simplified formulas for approximating these relations under the condition of relatively small sampling period are further developed. Thus, the numerical ranges of the sampled model parameters can then be predetermined roughly. Moreover, the tending-to-one theorems for the parameter sum of both the sampled model and its predictive version are also proved in a rigorous manner.
The main results obtained are very useful for the robust setf-tuning control, especially in presetting or resetting the initial values and deviation limits of the on-line recursive parameter estimation.