Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On second-order cone positive systems   Internal positivity offers a computationally cheap certificate for external
(input-output) positivity of a linear time-invariant system. However, the
drawback with this certificate lies in its realization dependency. Firstly,
computing such a realization requires to find a polyhedral cone with a
potentially high number of extremal generators that lifts the dimension of the
state-space representation, significantly. Secondly, not all externally
positive systems posses an internally positive realization. Thirdly, in many
typical applications such as controller design, system identification and model
order reduction, internal positivity is not preserved. To overcome these
drawbacks, we present a tractable sufficient certificate of external positivity
based on second-order cones. This certificate does not require any special
state-space realization: if it succeeds with a possibly non-minimal
realization, then it will do so with any minimal realization. While there exist
systems where this certificate is also necessary, we also demonstrate how to
construct systems, where both second-order and polyhedral cones as well as
other certificates fail. Nonetheless, in contrast to other realization
independent certificates, the present one appears to be favourable in terms of
applicability and conservatism. Three applications are representatively
discussed to underline its potential. We show how the certificate can be used
to find externally positive approximations of nearly externally positive
systems and demonstrated that this may help to reduce system identification
errors. The same algorithm is used then to design state-feedback controllers
that provide closed-loop external positivity, a common approach to avoid over-
and undershooting of the step response. Lastly, we present modifications to
generalized balanced truncation such that external positivity is preserved
where our certificate applies.

36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex