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General Inertia and Circle Criterion

Solmaz, Selim and Mason, Oliver and Shorten, Robert (2006) General Inertia and Circle Criterion. Proceedings in Applied Mathematics and Mechanics, 6 (1). pp. 845-846.

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In this paper we extend the well known Kalman-Yacubovic-Popov (KYP) lemma to the case of matrices with general regular inertia. We show that the version of the lemma that was derived for the case of pairs of stable matrices whose rank difference is one, extends to the more general case of matrices with regular inertia and in companion form. 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 that can be considered as a time-domain interpretation of the famous circle criterion.

Item Type: Article
Keywords: General Inertia, Matrices, Circle Criterion, Stability, Switching Systems
Subjects: Science & Engineering > Hamilton Institute
Science & Engineering > Mathematics & Statistics
Item ID: 883
Depositing User: Selim Solmaz
Date Deposited: 29 Jan 2008
Journal or Publication Title: Proceedings in Applied Mathematics and Mechanics
Refereed: Yes

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