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On integral linear constraints on convex cones

Vladu, Emil LU orcid ; Megretski, Alexandre and Rantzer, Anders LU orcid (2026) In Systems and Control Letters 216.
Abstract

In this paper, we consider integral linear constraints and the dissipation inequality with linear supply rates for certain sets of trajectories confined pointwise in time to a convex cone which belongs to a finite-dimensional normed vector space. Such constraints are then shown to be satisfied if and only if a bounded linear functional exists which satisfies a conic inequality. This is analogous to the typical situation in which a quadratic supply rate over the entire space is related to a linear matrix inequality. A connection is subsequently drawn precisely to linear–quadratic control: by proper choice of cone, the main results can be applied to produce a known L1-gain analogue to the bounded real lemma in positive systems... (More)

In this paper, we consider integral linear constraints and the dissipation inequality with linear supply rates for certain sets of trajectories confined pointwise in time to a convex cone which belongs to a finite-dimensional normed vector space. Such constraints are then shown to be satisfied if and only if a bounded linear functional exists which satisfies a conic inequality. This is analogous to the typical situation in which a quadratic supply rate over the entire space is related to a linear matrix inequality. A connection is subsequently drawn precisely to linear–quadratic control: by proper choice of cone, the main results can be applied to produce a known L1-gain analogue to the bounded real lemma in positive systems theory, as well as a non-strict version of the Kalman–Yakubovich–Popov Lemma in linear–quadratic control.

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author
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organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Convex cones, Linear–quadratic control, Positive systems
in
Systems and Control Letters
volume
216
article number
106509
publisher
Elsevier
external identifiers
  • scopus:105043906823
ISSN
0167-6911
DOI
10.1016/j.sysconle.2026.106509
language
English
LU publication?
yes
id
b81676bf-33da-4c9f-87fb-b13eb706d8b2
date added to LUP
2026-09-28 15:51:02
date last changed
2026-09-28 15:52:14
@article{b81676bf-33da-4c9f-87fb-b13eb706d8b2,
  abstract     = {{<p>In this paper, we consider integral linear constraints and the dissipation inequality with linear supply rates for certain sets of trajectories confined pointwise in time to a convex cone which belongs to a finite-dimensional normed vector space. Such constraints are then shown to be satisfied if and only if a bounded linear functional exists which satisfies a conic inequality. This is analogous to the typical situation in which a quadratic supply rate over the entire space is related to a linear matrix inequality. A connection is subsequently drawn precisely to linear–quadratic control: by proper choice of cone, the main results can be applied to produce a known L<sub>1</sub>-gain analogue to the bounded real lemma in positive systems theory, as well as a non-strict version of the Kalman–Yakubovich–Popov Lemma in linear–quadratic control.</p>}},
  author       = {{Vladu, Emil and Megretski, Alexandre and Rantzer, Anders}},
  issn         = {{0167-6911}},
  keywords     = {{Convex cones; Linear–quadratic control; Positive systems}},
  language     = {{eng}},
  publisher    = {{Elsevier}},
  series       = {{Systems and Control Letters}},
  title        = {{On integral linear constraints on convex cones}},
  url          = {{http://dx.doi.org/10.1016/j.sysconle.2026.106509}},
  doi          = {{10.1016/j.sysconle.2026.106509}},
  volume       = {{216}},
  year         = {{2026}},
}