Testing Reachability and Stabilizability of Systems over Polynomial Rings UsingGroebner Bases

摘要

Conditions for the reachability and stabilizability of systems over polynomialrings are well-known in the literature. For a system Sigma = (A,B) they can be expressed as right-invertibility conditions on the matrix (zI-A/B). Therefore, there is quite a strong algebraic relationship between both conditions, but unfortunately they are difficult to check explicitly. In this paper we introduce for each system Sigma = (A,B) a corresponding polynomial ideal Iota which characterizes both reachability and stabilizability in a very straightforward way. Moreover, methods are given to compute this ideal and its variety explicitly using Grobner Bases techniques. With the help of the Grobner Basis of the ideal Iota, conclusions on the reachability and stabilizability of the system Sigma = (A,B) are easy to draw.