A New Nonunique PSVD-Based Inverse of Nonsquare Polynomial Matrices

Abstract

A new nonunique inverse of nonsqure polynomial matrices is introduced in this paper. Following the new given definitions of ${T-, \tau-, \sigma-, S-}$ and $H$-inverse a new issue concerning the HM-inverse of plants having different number of input and output variables is presented. It is noted that a new method can be applied to the different nonsquare systems finally to obtain the inverse model control schemes known as the IMC structures. Additionally, it is emphasized that the authors' approach can be useful during design of perfect control strategy dedicated to LTI MIMO right-invertible objects. After some assumption the technique taken from perfect signal reconstruction tasks could be implemented in the minimum variance/perfect control problem and, crucially, stands as a counterpart to existing methods of signal recovery.