Weak feedback cyclizability and coefficient assignment for weakly reachable systems over a principal ideal domain

For a system defined over a ring, the property of weak reachability induces some restrictions to the coefficient assignability property of the system. In this paper it is proved that, for systems defined over a principal ideal domain, the invariant factors of the Smith form of the reachability matrix of the system play a key role in these restrictions, and actually characterize them. An example of application to time-delay systems is also presented.