Invariant factors and output feedback

The problem of assigning invariant factors by internally stable output feedback configurations is considered. The emphasis is placed on the input-output invariant factors of the final feedback configuration, whereas the internal hidden modes of the final system are disregarded after their stability is ensured. Two types of output feedback configurations are considered: (i) a combination of unity feedback and dynamic pre-compensation, and (ii) pure dynamic output feedback. It is shown that in both cases the possibilities of assigning invariant factors depend on certain integer invariants which are determined, roughly speaking, by the unstable poles, by the unstable zeros, and by the zeros at infinity of the transfer matrix of the given system.