Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

On the Kalman-Yakubovich-Popov Lemma for Positive Systems

Rantzer, Anders LU (2016) In IEEE Transactions on Automatic Control 61(5). p.1346-1349
Abstract
An extended Kalman-Yakubovich-Popov (KYP) Lemma for positive systems is derived. The main difference compared to earlier versions is that non-strict inequalities are treated. Matrix assumptions are also less restrictive. Moreover, a new equivalence is introduced in terms of linear programming rather than semi-definite programming. As a complement to the KYP lemma, it is also proved that a symmetric Metzler matrix with m non-zero entries above the diagonal is negative semi-definite if and only if it can be written as a sum of m negative semi-definite matrices, each of which has only four non-zero entries. This is useful in the context large-scale optimization.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
IEEE Transactions on Automatic Control
volume
61
issue
5
pages
1346 - 1349
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:84964691324
  • wos:000375120500019
ISSN
0018-9286
DOI
10.1109/TAC.2015.2465571
project
LCCC
language
English
LU publication?
yes
id
3d8392d0-9979-48bf-9db3-40131b92a3d0 (old id 8167160)
date added to LUP
2016-04-04 13:57:56
date last changed
2022-05-02 00:55:36
@article{3d8392d0-9979-48bf-9db3-40131b92a3d0,
  abstract     = {{An extended Kalman-Yakubovich-Popov (KYP) Lemma for positive systems is derived. The main difference compared to earlier versions is that non-strict inequalities are treated. Matrix assumptions are also less restrictive. Moreover, a new equivalence is introduced in terms of linear programming rather than semi-definite programming. As a complement to the KYP lemma, it is also proved that a symmetric Metzler matrix with m non-zero entries above the diagonal is negative semi-definite if and only if it can be written as a sum of m negative semi-definite matrices, each of which has only four non-zero entries. This is useful in the context large-scale optimization.}},
  author       = {{Rantzer, Anders}},
  issn         = {{0018-9286}},
  language     = {{eng}},
  number       = {{5}},
  pages        = {{1346--1349}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{IEEE Transactions on Automatic Control}},
  title        = {{On the Kalman-Yakubovich-Popov Lemma for Positive Systems}},
  url          = {{http://dx.doi.org/10.1109/TAC.2015.2465571}},
  doi          = {{10.1109/TAC.2015.2465571}},
  volume       = {{61}},
  year         = {{2016}},
}