Feedback stabilization over commutative rings: two-stage feedback stabilization approach

Two criteria of the feedback stabilizability for MIMO systems over a commutative ring are given. Both of them are generalizations of Sule's results (1994). The first criterion is presented in terms of modules generated from a plant and does not require the plant be strictly causal. It shows that if the plant is stabilizable the modules are projective. The other criterion is presented in terms of ideals called the generalized elementary factors. This gives the stabilizability of a plant in terms of the coprimeness of the generalized elementary factors. These results are based on an assumption on the commutative ring which is that the set of all zero divisors is an ideal. This assumption is weaker than the assumption of previous results.