Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Obstructions to Genericity in Study of Parametric Problems in Control
  Theory   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.

10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex