On the properties of linear multirate systems with coprime output rates

This paper studies discrete-time linear systems with multirate outputs, assuming that two measured output streams are available at coprime rates. In the literature this type of system, which can be considered as periodic time-varying, is commonly studied in its blocked version, since the well-known techniques of analysis developed for linear time-invariant systems can be used. In particular, we focus on some structural properties of the blocked systems and we prove that, under a generic setting i.e. for a generic choice of parameter matrices, the blocked systems are minimal when the underlying multirate system is defined using a minimal dimension system. Moreover, we focus on zeros of tall blocked systems i.e. blocked systems with more outputs than inputs. In particular, we study those cases where the associated system matrix attains full-column rank. We exhibit situations where they generically have no finite nonzero zeros.