Absolute instability of Lur'e systems and its application to oscillation analysis of uncertain genetic networks. (17th December 2014)

• Record Type: Journal Article
• Authors: Inoue, Masaki; Imura, Jun‐ichi; Kashima, Kenji; Suzuki, Masayasu; Aihara, Kazuyuki
• Is Part Of: International journal of robust and nonlinear control. Volume 25:Number 18(2015)
• Page Start: 3746
• Page End: 3762
• Publication Date: 2014-12-17
• Subjects: absolute instability -- Lur'e systems -- uncertain systems -- biological systems; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.3294
• Languages: English
• ISSNs: 1049-8923

Abstract

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.