Feedback stabilization over commutative rings: further study of the coordinate-free approach

The paper is concerned with the coordinate-free approach to control systems. We present two criteria for feedback stabilizability for MIMO systems in which transfer functions belong to the total rings of fractions of commutative rings. The first criterion is expressed in terms of modules generated from a causal plant and does not require the plant to be strictly causal. It shows that if the plant is stabilizable, the modules are projective. The other criterion is expressed in terms of ideals called generalized elementary factors. This gives the stabilizability of a causal plant in terms of the coprimeness of the generalized elementary factors.