The Effective Calculation of All Assignable Polynomials to a Single-Input System Over a BÉzout Domain

The set of all feedback assignable polynomials to a given single input system over a Bezout domain is obtained. The general case is reduced to the case of weakly reachable systems, for these systems a canonical form for the algebraic equivalence is obtained. Algorithms and examples over a Euclidean domain and in particular over the ring Z of rational integers are also given. The problem of deciding and feedback assignment of a given polynomial to a given non-reachable n dimensional linear system is solved effectively up to a cost of O(n⁴) arithmetic operations.