Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Diagonal Stability of $k$-Positive Linear Systems   We consider $k$-positive linear systems, that is, systems that map the set of
vectors with up to $k-1$ sign variations to itself. For $k=1$, this reduces to
positive linear systems. It is well-known that stable positive linear time
invariant (LTI) systems admit a diagonal Lyapunov function. This property has
many important implications. A natural question is whether stable $k$-positive
systemsalso admit a diagonal Lyapunov function. This paper shows that, in
general, the answer is no. However, for both continuous-time and discrete-time
$n$-dimensional systems that are $(n-1)$-positive we provide a sufficient
condition for diagonal stability.

31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th