Absolute instability of Lur'e systems and its application to oscillation analysis of uncertain genetic networks

Masaki Inoue, Jun Ichi Imura, Kenji Kashima, Masayasu Suzuki, Kazuyuki Aihara

Research output: Contribution to journalArticle


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.

Original languageEnglish
Pages (from-to)3746-3762
Number of pages17
JournalInternational Journal of Robust and Nonlinear Control
Issue number18
Publication statusPublished - 2015 Dec 1



  • absolute instability
  • biological systems
  • Lur'e systems
  • uncertain systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering
  • Chemical Engineering(all)
  • Mechanical Engineering
  • Aerospace Engineering
  • Biomedical Engineering
  • Industrial and Manufacturing Engineering

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