A simple derivation of interactor matrix and its applications

An interactor matrix plays several important roles in the control system theory. In this paper, we present a simple method to derive the special interactor matrix using Moore-Penrose pseudo-inverse. The interactor derived by the proposed method has all its zeros at the origin, and has the all-pass property in the discrete-time. It is shown that the feedback gain of the inverted interactor using the canonical interactor is equivalent to the LQ optimal gain for singular weighting. A systematic procedure to obtain the identity interactor, which has the arbitrarily pre-specified zeros, is also shown.