On the Kalman-Yakubovich-Popov Lemma for Positive Systems
(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:
https://lup.lub.lu.se/record/8167160
- author
- Rantzer, Anders LU
- organization
- publishing date
- 2016
- 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
- 2024-03-30 21:30:24
@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}}, }