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On the Kalman-Yakubovich-Popov Lemma for Positive Systems

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Author

Summary, in English

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.

Publishing year

2016

Language

English

Pages

1346-1349

Publication/Series

IEEE Transactions on Automatic Control

Volume

61

Issue

5

Document type

Journal article

Publisher

IEEE - Institute of Electrical and Electronics Engineers Inc.

Topic

  • Control Engineering

Status

Published

Project

  • LCCC

Research group

  • LCCC

ISBN/ISSN/Other

  • ISSN: 0018-9286