Abstract
When the plant transfer matrix is given by T(s), the interactor L(s) is the polynomial matrix which makes L(s)T(s) a full rank constant matrix as s tends to infinity. The interactor matrix has an important role for the design of the exact model matching control and the adaptive control for the linear multivariable systems. It was first defined by Wolovich and Falb as a lower left triangular polynomial matrix whose diagonal elements are monomials.
In this paper, the structure and the derivation algorithm of the generalized lower left interactor matrix are discussed in detail using the new concepts of di-column properness and di-improperness index of a polynomial matrix. The algebraic relation of the coefficient matrices between the generalized interactor and the plant transfer matrix is obtained. Based on this relation, it is shown that the diagonal elements of the generalized interactor can be chosen as arbitrary polynomials of adequate degrees which are given by di-improperness indices calculated in each stage of the derivation algorithm, and that once the diagonal elements are chosen, the off diagonal elements (lower left part) are determined uniquely except the constant terms. This generalized interactor contains the interactor matrix proposed by Wolovich and Falb as a special case.
