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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.
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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
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
2015-11-06 18:48:31
date last changed
2017-04-30 16:56:54
@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},
  volume       = {61},
  year         = {2016},
}