Right/Left inverses of polynomial matrices for control, communications and vision

Abstract

This paper reviews various right/left inverses of polynomial matrices, introduced by the authors as a result of their research works on minimum variance control for LTI MIMO systems. In consequence, a new, general, Smith-factorization based inverse is presented. The problem of selection of stable inverses, in particular pole-free inverses, is also tackled. Applications in control, communications and vision, in particular concerning perfect signal transmission/recovery, are indicated.Index Terms-MIMO channels/systems, right/left inverses of polynomial matrices, Smith factorization, minimum variance control.