On the zero properties of linear discrete-time systems with multirate outputs

In this paper the zero properties of discrete-time linear systems with multirate outputs are studied. In the literature the zero properties of these systems are defined as those of their corresponding time-invariant blocked systems. Hence, the focus is on the zero properties of blocked systems resulting from blocking of linear systems with multirate outputs. In particular, we study the zero properties of tall blocked systems under a generic setting i.e. for generic parameter matrices; moreover, we only study the zero properties for choice of finite zeros. We demonstrate that tall blocked systems generically have no finite nonzero zeros. We then show when tall blocked systems can generically be zero-free at the origin i.e. Z = 0, and when they must have zeros at that point.