Improvement of generalized elementary factors and new criteria of the feedback stabilizability over integral domain

Recently, a theory of the feedback stabilization of MIMO transfer matrices in terms of elementary factors over a unique factorization domain was developed by Sule [SIAM J. Control Optim., 32-6, 1675-1695(1994)]. The authors enlarged the concept of "elementary factor" by introducing the concept of "generalized elementary factor." Both concepts are defined based on two matrices [N^T dE_m]^T and [N dE_n], where P = Nd^-1 is a transfer matrix of a given plant, N (d) is a stable causal transfer matrix (function), and E_m (E_n) is the identity matrix of size m (n). In this paper, we show that for the feedback stabilizability of a given plant, it is sufficient to consider one of the matrices [N^T dE_m]^T or [N dE_n].