On the Zero Properties of Tall Linear Systems with Single-rate and Multirate Outputs
Brian D. O. Anderson, Mohsen Zamani, Giulio Bottegal · ANU Open Research (Australian National University) · 2013
The zero properties of tall discrete-time multirate linear systems are studied in this paper. In the literature, zero properties of multirate linear systems are defined as those of their corresponding blocked systems, which are time-invariant systems whose behavior is broadly equivalent to that of the generating multirate system. In this paper, we review some recent scattered results of the authors and their colleagues dealing with the zero properties of the blocked systems associated with multirate systems. First, we show that tall linear time-invariant unblocked systems are zero-free when the parameter matrices A,B,C,D assume generic values. Then it is argued that tall blocked systems obtained from blocking of tall linear timeinvariant systems with generic parameter matrices A,B,C,D, are also zero-free. Finally, we illustrate that tall blocked systems associated with multirate systems generically have no finite nonzero zeros.