Coprime sampling for system stabilization with FIR multirate controllers

Coprime sampling has in the past found applications in fractional sampling rate alteration, spatial array processing, radar signal processing, system identification, and fractionally spaced channel-equalization. This paper revisits multirate feedback control systems in the context of coprime sampling theory. It is shown in particular that the system from the primary input to the output node can be stabilized with an FIR controller when the feedback rate is higher than the input and output rates. On the other hand, the system from the primary input to the feedback signal node can be stabilized with an FIR controller, whether the feedback rate is higher or lower than the input and output rates. These results hold under a coprimality assumption on certain transfer matrices which arise in the plant description. The assumption is mild in the sense that it is almost always satisfied in practice.