Time delay systems have the mathematical difficulties for the controller design, the modeling and so on. In the continuous time approach, a time delay system has an infinite dimension. On the other hand, in the discrete time approach, an input time delay system has finite dimension and many controller design methods for the finite dimensional systems can be applied. But, for the case that the length of a time delay is not multiples of a discrete time, some additional methods are needed. The modeling and controller design methods have been studied by some authors for this case.
In this paper, we focus on the case that the delay length is not multiples of a discrete time. Then the discrete time model is derived for the input and unilateral time delay systems without any approximations.
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