An explicit solution to the discrete-time singular LQ regulation problem for a plant having more inputs than the outputs

In this paper, an explicit solution to the discrete-time singular LQ problem for a plant having more inputs than the outputs is discussed. It is shown that the solution is given by an inverted interactorizing gain for the minimum phase image of some squarizing systems. An interactor matrix plays an important role for squarizing of a given plant. Also shown is a derivation of minimum phase image for a given plant using the generalized interactor.