Parametrization of Generalized Interactors and Its Relation to the Discrete-Time All-Pass Property

Abstract

This paper gives a concise parametrization of all generalized interactors of a discrete-time multivariable system. This is done by using state-space description of a given particular interactor. The paper then proposes a selection of the parameter which leads to an all-pass closed-loop transfer matrix. This closed-loop system turns out to be equivalent to an LQ optimal feedback system. A numerical example is given to illustrate the results.