  This paper is concerned with the coordinate-free approach to control systems.
The coordinate-free approach is a factorization approach but does not require
the coprime factorizations of the plant. We present two criteria for feedback
stabilizability for MIMO systems in which transfer functions belong to the
total rings of fractions of commutative rings. Both of them are generalizations
of Sule's results in [SIAM J. Control Optim., 32-6, 1675-1695(1994)]. 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. As an example, a discrete finite-time delay
system is considered.
