A KYP lemma for LMI regions

Brandon Hencey; Andrew G. Alleyne

doi:10.1109/TAC.2007.906222

A KYP lemma for LMI regions

Brandon Hencey, Andrew G. Alleyne

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

In this technical note, a Kalman-Yakubovich-Popov (KYP) lemma is discussed for linear matrix inequality (LMI) regions. Sufficient quadratic stability conditions are developed for an uncertain linear system subject to time varying uncertainty satisfying a quadratic inequality. Furthermore, the quadratic stability conditions are shown to guarantee the satisfaction of a frequency domain inequality.

Original language	English (US)
Pages (from-to)	1926-1930
Number of pages	5
Journal	IEEE Transactions on Automatic Control
Volume	52
Issue number	10
DOIs	https://doi.org/10.1109/TAC.2007.906222
State	Published - Oct 2007
Externally published	Yes

Bibliographical note

Funding Information:
Manuscript received January 9, 2006; revised July 12, 2006; March 13, 2007; and May 31, 2007. Recommended by Associate Editor G. Chesi. This work was supported in part by Caterpillar, Inc. and by the Army Research Office by Grant W911NF-04-1-0067.

Keywords

Kalman-Yakubovich-Popov (KYP) lemma
Linear matrix inequality (LMI)
Regional pole placement
Uncertainty

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10.1109/TAC.2007.906222

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title = "A KYP lemma for LMI regions",

abstract = "In this technical note, a Kalman-Yakubovich-Popov (KYP) lemma is discussed for linear matrix inequality (LMI) regions. Sufficient quadratic stability conditions are developed for an uncertain linear system subject to time varying uncertainty satisfying a quadratic inequality. Furthermore, the quadratic stability conditions are shown to guarantee the satisfaction of a frequency domain inequality.",

keywords = "Kalman-Yakubovich-Popov (KYP) lemma, Linear matrix inequality (LMI), Regional pole placement, Uncertainty",

author = "Brandon Hencey and Alleyne, {Andrew G.}",

note = "Funding Information: Manuscript received January 9, 2006; revised July 12, 2006; March 13, 2007; and May 31, 2007. Recommended by Associate Editor G. Chesi. This work was supported in part by Caterpillar, Inc. and by the Army Research Office by Grant W911NF-04-1-0067.",

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language = "English (US)",

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AU - Alleyne, Andrew G.

N1 - Funding Information: Manuscript received January 9, 2006; revised July 12, 2006; March 13, 2007; and May 31, 2007. Recommended by Associate Editor G. Chesi. This work was supported in part by Caterpillar, Inc. and by the Army Research Office by Grant W911NF-04-1-0067.

PY - 2007/10

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N2 - In this technical note, a Kalman-Yakubovich-Popov (KYP) lemma is discussed for linear matrix inequality (LMI) regions. Sufficient quadratic stability conditions are developed for an uncertain linear system subject to time varying uncertainty satisfying a quadratic inequality. Furthermore, the quadratic stability conditions are shown to guarantee the satisfaction of a frequency domain inequality.

AB - In this technical note, a Kalman-Yakubovich-Popov (KYP) lemma is discussed for linear matrix inequality (LMI) regions. Sufficient quadratic stability conditions are developed for an uncertain linear system subject to time varying uncertainty satisfying a quadratic inequality. Furthermore, the quadratic stability conditions are shown to guarantee the satisfaction of a frequency domain inequality.

KW - Kalman-Yakubovich-Popov (KYP) lemma

KW - Linear matrix inequality (LMI)

KW - Regional pole placement

KW - Uncertainty

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JF - IEEE Transactions on Automatic Control

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ER -

A KYP lemma for LMI regions

Abstract

Bibliographical note

Keywords

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