Both of an interactor and zeros at infinity of multivariable systems are the generalized concepts of a relative degree of a scalar transfer function. Although it seems that these concepts are exactly the same, the former has been used for design of various types of control systems, while the latter are used for analyzing control systems. In the scalar case, the degree of an interactor is the same as the order of zero at infinity of a given plant. But, it is not always true in the multivariable case. This paper concerns the relation between the structure of degrees of an interactor and the orders of zeros at infinity of a given transfer matrix. If the structure of degrees of an interactor coincides with the orders of zeros at infinity of a given plant, it is called a regular interactor. In terms of this, it is shown that any transfer matrix has its equivalent form which has a regular interactor. This equivalent form can be obtained by suitable interchanges of rows of the transfer matrix. It is also shown that a regular interactor is row proper.
This paper also includes inverted interactorizing by state feedback which is the basic structure of various types of multivariable control systems. Especially, the exact model matching control and the decoupling control systems can be regarded as special cases of inverted interactorizing. Finally, a method is proposed to estimate a structure of a regular interactor for a plant with unknown parameters, which is an important technique for the adaptive case.
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