On the Kalman-Yakubovich-Popov Lemma for Positive Systems

Research output: Contribution to journalArticle


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 languageEnglish
Pages (from-to)1346-1349
JournalIEEE Transactions on Automatic Control
Issue number5
Publication statusPublished - 2016

Subject classification (UKÄ)

  • Control Engineering


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