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A Cone-preserving Solution to a Nonsymmetric Riccati Equation

Vladu, Emil LU orcid and Rantzer, Anders LU orcid (2025) In Linear Algebra and Its Applications 709. p.449-459
Abstract
In this paper, we provide the following simple equivalent condition for a nonsymmetric Algebraic Riccati Equation to admit a stabilizing cone-preserving solution: an associated coefficient matrix must be stable. The result holds under the assumption that said matrix be cross-positive on a proper cone, and it both extends and completes a corresponding sufficient condition for nonnegative matrices in the literature. Further, key to showing the above is the following result which we also provide: in order for a monotonically increasing sequence of cone-preserving matrices to converge, it is sufficient to be bounded above in a single vectorial direction.
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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Nonsymmetric Algebraic Riccati Equations, Cross-positivity
in
Linear Algebra and Its Applications
volume
709
pages
11 pages
publisher
Elsevier
external identifiers
  • scopus:85216090660
ISSN
1873-1856
DOI
10.1016/j.laa.2025.01.020
project
Throughput Control in Autonomous Networks
language
English
LU publication?
yes
id
bbd08f0d-770e-4926-98e4-51e829edcd00
date added to LUP
2025-02-24 15:04:04
date last changed
2025-04-04 14:25:33
@article{bbd08f0d-770e-4926-98e4-51e829edcd00,
  abstract     = {{In this paper, we provide the following simple equivalent condition for a nonsymmetric Algebraic Riccati Equation to admit a stabilizing cone-preserving solution: an associated coefficient matrix must be stable. The result holds under the assumption that said matrix be cross-positive on a proper cone, and it both extends and completes a corresponding sufficient condition for nonnegative matrices in the literature. Further, key to showing the above is the following result which we also provide: in order for a monotonically increasing sequence of cone-preserving matrices to converge, it is sufficient to be bounded above in a single vectorial direction.}},
  author       = {{Vladu, Emil and Rantzer, Anders}},
  issn         = {{1873-1856}},
  keywords     = {{Nonsymmetric Algebraic Riccati Equations; Cross-positivity}},
  language     = {{eng}},
  month        = {{02}},
  pages        = {{449--459}},
  publisher    = {{Elsevier}},
  series       = {{Linear Algebra and Its Applications}},
  title        = {{A Cone-preserving Solution to a Nonsymmetric Riccati Equation}},
  url          = {{http://dx.doi.org/10.1016/j.laa.2025.01.020}},
  doi          = {{10.1016/j.laa.2025.01.020}},
  volume       = {{709}},
  year         = {{2025}},
}