On the zero-freeness of tall multirate linear systems

In this technical note, tall discrete-time linear systems with multirate outputs are studied. In particular, we focus on their zeros. In systems and control literature zeros of multirate systems are defined as those of their corresponding time-invariant systems obtained through blocking of the original multirate systems. We assume that blocked systems are tall, i.e., have more outputs than inputs. It is demonstrated that, for generic choice of the parameter matrices, linear systems with multirate outputs generically have no finite nonzero zeros. However, they may have zeros at the origin or at infinity depending on the choice of blocking delay and the input, state and output dimensions.