Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On two natural extensions of Vinnicombe's metric: their noncoincidence
  yet equivalence on stabilizable plants over A_+   Let A_+ be the ring of Laplace transforms of complex Borel measures on R with
support in [0,+\infty) which do not have a singular nonatomic part. We compare
the nu-metric d_{A_+} for stabilizable plants over A_+ given in the article by
Ball and Sasane [2010], with yet another metric d_{H^\infty}|_{A_+}, namely the
one induced by the metric d_{H^\infty} for the set of stabilizable plants over
H^\infty given in teh article by Sasane in 2011. Both d_{A_+} and d_{H^\infty}
coincide with the classical Vinnicombe metric defined for rational transfer
functions, but we show here by means of an example that these two possible
extensions of the classical nu-metric for plants over A_+ do not coincide on
the set of stabilizable plants over A_+. We also prove that they nevertheless
give rise to the same topology on stabilizable plants over A_+, which in turn
coincides with the gap metric topology.

13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph