Parametrization of identity interactors and the discrete-time all-pass property

This paper gives a concise parametrization of all identity interactors of a discrete-time multivariable square system. This is performed by means of a state-space description computed from a given particular interactor of the system. 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 a certain LQ (linear quadratic) optimal feedback system. A numerical example is given to illustrate the results.