Reachability Test for Systems over Polynomial Rings Using Groebner Bases

摘要

Conditions for the reachability of a system over a polynomial ring are well knownin the literature. However, the verification of these conditions remained a difficult problem in general. Application of the Grobner Basis method from constructive commutative algebra makes it possible to carry out this test explicitly. In this paper it is shown how this can be done in an efficient way. In comparison with a very simple and rather straightforward method, the algorithm proposed in this paper has an enormous advantage: it has a good performance for both reachable and non-reachable systems. Moreover, the method can be used to