On the Structure at Infinity and the Structure of an Interactor

Abstract

Since an interactor is defined as a polynomial matrix which cancels all zeros at infinity of a given plant transfer matrix by multiplying from the left, an interactor can be regarded as an alternative representation of the structure at infinity of a plant. This implies that there is a direct relationship between the structure at infinity of a plant and the structure of degrees of its interactor. In this paper, we will discuss this relationship. For this purpose, we define a regular interactor by an interactor whose row degrees coincide with the multiplicities of zeros at infinity of a plant. Then, it will be shown that an interactor is regular if and only if it is row proper. We will also give a procedure for calculating a regular interactor from a given transfer matrix.

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