Generalizing the KYP Lemma to Multiple Frequency Intervals | Zendy

Goele Pipeleers | Zendy; Tetsuya Iwasaki | Zendy; Shinji Hara | Zendy

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Generalizing the KYP Lemma to Multiple Frequency Intervals

Author(s) -

Goele Pipeleers,

Tetsuya Iwasaki,

Shinji Hara

Publication year - 2014

Publication title -

siam journal on control and optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.486

H-Index - 116

eISSN - 1095-7138

pISSN - 0363-0129

DOI - 10.1137/130938451

Subject(s) - mathematics , lemma (botany) , equivalence (formal languages) , complex plane , generalization , polynomial , mathematical analysis , pure mathematics , ecology , poaceae , biology

A recent generalization of the Kalman--Yakubovich--Popov (kyp) lemma establishes the equivalence between a semi-infinite inequality on a segment of a circle or straight line in the complex plane and a linear matrix inequality. In this paper we further generalize the kyp lemma to particular curves in the complex plane, described by a polynomial equality and a polynomial inequality that satisfy certain conditions. The considered set of curves is shown to include the union of segments of a circle or line as a special case.

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