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General Inertia and Circle Criterion
Author(s) -
Solmaz Selim,
Mason Oliver,
Shorten Robert
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610402
Subject(s) - lemma (botany) , inertia , mathematics , interpretation (philosophy) , rank (graph theory) , verifiable secret sharing , pure mathematics , combinatorics , computer science , physics , classical mechanics , ecology , poaceae , set (abstract data type) , biology , programming language
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. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)