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On the Kalman-Yakubovich-Popov lemma and common Lyapunov solutions for matrices with regular inertia

Mason, Oliver and Shorten, Robert and Solmaz, Selim (2007) On the Kalman-Yakubovich-Popov lemma and common Lyapunov solutions for matrices with regular inertia. Linear Algebra and its Applications, 420 (1). pp. 183-197.

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Abstract

In this paper we extend the classical Lefschetz version of the Kalman-Yacubovich-Popov (KYP) lemma to the case of matrices with general regular inertia. We then use this result to derive an easily verifiable spectral condition for a pair of matrices with the same regular inertia to have a common Lyapunov solution (CLS), extending a recent result on CLS existence for pairs of Hurwitz matrices.

Keywords:General Inertia, KYP Lemma, Circle Criterion, Stability, Switched Systems
Subjects:Science & Engineering > Hamilton Institute
Science & Engineering > Mathematics
ID Code:885
Deposited By:Selim Solmaz
Deposited On:29 Jan 2008
Journal or Publication Title:Linear Algebra and its Applications
Refereed:Yes
URL:http://www.hamilton.ie/selim/index.html, http://www.hamilton.ie/publications.htm

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