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This paper presents several new results on the inversion of full normal rank nonsquare polynomial matrices. New analytical right/left inverses of polynomial matrices are introduced, including the so-called ? -inverses, ?-inverses and, in particular, S-inverses, the latter providing the most general tool for the design of various polynomial matrix inverses. The pplicationoriented problem of selecting stable inverses is also solved. Applications in inverse-model control, in particular robust minimum variance control, are exploited, and possible applications in signal transmission/recovery in various types of MIMO channels are indicated.