Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the stability and null-controllability of an infinite system of
  linear differential equations   In this work, the null controllability problem for a linear system in
$\ell^2$ is considered, where the matrix of a linear operator describing the
system is an infinite matrix with $\lambda\in \mathbb R$ on the main diagonal
and 1s above it. We show that the system is asymptotically stable if and only
if $\lambda\le-1$, which shows the fine difference between the finite and the
infinite-dimensional systems. When $\lambda\le-1$ we also show that the system
is null controllable in large. We also show a dependence of the stability on
the norm i.e. the same system considered in $\ell^\infty$ is not asymptotically
stable if $\lambda=-1$.

3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin