New algorithm to construct a stabilizing controller for linear systems over integral domains

We are concerned with the coordinate-free approach to controlsystems, which is a factorization approach but does not requirethe coprime factorizations of plants, provided only that theset of stable causal transfer functions forms an integral domain.We first present a new criterion of the feedback stabilizability.This is a generalization of the criteria in terms of reducedminors given by Sule in 1994 and in terms of quotient idealsgiven by Shankar and Sule in 1992. We then present an algorithmto construct a stabilizing controller, which is derived fromthe result given by Lin in 1998. Sule's algorithm and its derivationsneed to convert some matrices over some ring of fractions toones over the set of stable causal transfer functions, whichmay raise the unnecessarily complicated calculations. On theother hand, the algorithm of this paper does not require sucha conversion. An illustrative example to construct a stabilizingcontroller is also presented.