We investigate systems of equations, involving parameters from the point of
view of both control theory and computer algebra. The equations might involve
linear operators such as partial (q-)differentiation, (q-)shift, (q-)difference
as well as more complicated ones, which act trivially on the parameters. Such a
system can be identified algebraically with a certain left module over a
non-commutative algebra, where the operators commute with the parameters. We
develop, implement and use in practice the algorithm for revealing all the
expressions in parameters, for which e.g. homological properties of a system
differ from the generic properties. We use Groebner bases and Groebner basics
in rings of solvable type as main tools. In particular, we demonstrate an
optimized algorithm for computing the left inverse of a matrix over a ring of
solvable type. We illustrate the article with interesting examples. In
particular, we provide a complete solution to the "two pendula, mounted on a
cart" problem from the classical book of Polderman and Willems, including the
case, where the friction at the joints is essential . To the best of our
knowledge, the latter example has not been solved before in a complete way.Comment: 20 page
