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Absolute instability of Lur'e systems and its application to oscillation analysis of uncertain genetic networks
Author(s) -
Inoue Masaki,
Imura Junichi,
Kashima Kenji,
Suzuki Masayasu,
Aihara Kazuyuki
Publication year - 2015
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3294
Subject(s) - instability , control theory (sociology) , equilibrium point , mathematics , parametric statistics , computer science , mathematical analysis , physics , statistics , control (management) , artificial intelligence , mechanics , differential equation
Summary We derive instability criteria for Lur'e systems with sector‐bounded nonlinearities and uncertain external signals. First, we define absolute instability of an equilibrium and derive an absolute instability condition for a fixed equilibrium point in terms of a linear matrix inequality, which is analogous to the well‐known circle stability criterion. Then, the condition is extended to a parametric absolute instability condition, which is applicable to the instability test of a Lur'e system with an equilibrium point whose location is affected by uncertain nonlinearities and uncertain external signals. Finally, we show that the proposed analysis method is useful through the oscillation analysis of an uncertain genetic network model. Copyright © 2014 John Wiley & Sons, Ltd.