On the Kalman-Yakubovich-Popov Lemma for Positive Systems

Anders Rantzer

doi:10.1109/TAC.2015.2465571

On the Kalman-Yakubovich-Popov Lemma for Positive Systems

Research output: Contribution to journal › Article

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.

Original language	English
Pages (from-to)	1346-1349
Journal	IEEE Transactions on Automatic Control
Volume	61
Issue number	5
DOIs	https://doi.org/10.1109/TAC.2015.2465571
Publication status	Published - 2016

Subject classification (UKÄ)

Control Engineering

Access to Document

10.1109/TAC.2015.2465571

LCCC
Holmqvist, A. (Researcher), Andersson, N. (Researcher), Cervin, A. (Researcher), Mannesson, A. (Researcher), Gattami, A. (Researcher), Ghulchak, A. (Researcher), Papadopoulos, A. V. (Researcher), Rantzer, A. (Researcher), Robertsson, A. (Researcher), Sootla, A. (Researcher), THEORIN, A. (Researcher), Bernhardsson, B. (Researcher), Olofsson, B. (Researcher), Wittenmark, B. (Researcher), Grussler, C. (Researcher), Johnsson, C. (Researcher), MADJIDIAN, D. (Researcher), Johannesson, E. (Researcher), Magnusson, F. (Researcher), Ståhl, F. (Researcher), Como, G. (Researcher), Chasparis, G. (Researcher), Turesson, G. (Researcher), Dressler, I. (Researcher), Åkesson, J. (Researcher), Cho, J. H. (Researcher), Årzén, K.-E. (Researcher), Åström, K. J. (Researcher), Sou, K. C. (Researcher), Mårtensson, K. (Researcher), Berntorp, K. (Researcher), Soltesz, K. (Researcher), Lessard, L. (Researcher), Hast, M. (Researcher), Rönn, M. (Researcher), Ansbjerg Kjær, M. (Researcher), Maggio, M. (Researcher), Kristalny, M. (Researcher), Garpinger, O. (Researcher), From, P. J. (Researcher), Larsson, P.-O. (Researcher), Giselsson, P. (Researcher), Johansson, R. (Researcher), Hägglund, T. (Researcher), Vladimerou, V. (Researcher), Romero Segovia, V. (Researcher), Aurelius, A. (Researcher), Cedersjö, G. (Researcher), Bür, K. (Researcher), Dellkrantz, M. (Researcher), Du, M. (Researcher), Amani, P. (Researcher), Larsson, R. (Researcher), Tärneberg, W. (Research student), Li, Z. (Researcher), Yin, L. (Researcher), Tufvesson, F. (Researcher), Höst, S. (Researcher), Nilsson, B. (Researcher), Stenström, S. (Researcher), Andersson, J. A. (Researcher), Diehl, S. (Researcher), Dürango, J. (Researcher), Ghazaei Ardakani, M. (Researcher), Forsberg, P.-O. (Researcher), Bengtsson, F. (Researcher), Jörntell, H. (Researcher), Arévalo, C. (Researcher), Führer, C. (Researcher), Andersson, C. (Researcher), Mohammadi, F. (Researcher), Ödling, P. (Researcher), Andersson, M. (Researcher), Kihl, M. (Researcher) & Tunestål, P. (Researcher)
2008/07/01 → 2018/06/30
Project: Research

Cite this

@article{3d8392d0997948bf9db340131b92a3d0,

title = "On the Kalman-Yakubovich-Popov Lemma for Positive Systems",

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 = "Anders Rantzer",

year = "2016",

doi = "10.1109/TAC.2015.2465571",

language = "English",

volume = "61",

pages = "1346--1349",

journal = "IEEE Transactions on Automatic Control",

issn = "0018-9286",

publisher = "IEEE - Institute of Electrical and Electronics Engineers Inc.",

number = "5",

}

TY - JOUR

T1 - On the Kalman-Yakubovich-Popov Lemma for Positive Systems

AU - Rantzer, Anders

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

U2 - 10.1109/TAC.2015.2465571

DO - 10.1109/TAC.2015.2465571

M3 - Article

SN - 0018-9286

VL - 61

SP - 1346

EP - 1349

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 5

ER -

On the Kalman-Yakubovich-Popov Lemma for Positive Systems

Abstract

Subject classification (UKÄ)

Access to Document

Fingerprint

Projects

LCCC

Cite this