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

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.

Original languageEnglish
Pages (from-to)3746-3762
Number of pages17
JournalInternational Journal of Robust and Nonlinear Control
Volume25
Issue number18
DOIs
Publication statusPublished - 2015 Dec 1

Fingerprint

Stability criteria
Linear matrix inequalities

Keywords

  • 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

Cite this

Absolute instability of Lur'e systems and its application to oscillation analysis of uncertain genetic networks. / Inoue, Masaki; Imura, Jun Ichi; Kashima, Kenji; Suzuki, Masayasu; Aihara, Kazuyuki.

In: International Journal of Robust and Nonlinear Control, Vol. 25, No. 18, 01.12.2015, p. 3746-3762.

Research output: Contribution to journalArticle

Inoue, Masaki ; Imura, Jun Ichi ; Kashima, Kenji ; Suzuki, Masayasu ; Aihara, Kazuyuki. / Absolute instability of Lur'e systems and its application to oscillation analysis of uncertain genetic networks. In: International Journal of Robust and Nonlinear Control. 2015 ; Vol. 25, No. 18. pp. 3746-3762.
@article{fce2ac9b934346fc975dd8d4dd7d5dc2,
title = "Absolute instability of Lur'e systems and its application to oscillation analysis of uncertain genetic networks",
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.",
keywords = "absolute instability, biological systems, Lur'e systems, uncertain systems",
author = "Masaki Inoue and Imura, {Jun Ichi} and Kenji Kashima and Masayasu Suzuki and Kazuyuki Aihara",
year = "2015",
month = "12",
day = "1",
doi = "10.1002/rnc.3294",
language = "English",
volume = "25",
pages = "3746--3762",
journal = "International Journal of Robust and Nonlinear Control",
issn = "1049-8923",
publisher = "John Wiley and Sons Ltd",
number = "18",

}

TY - JOUR

T1 - Absolute instability of Lur'e systems and its application to oscillation analysis of uncertain genetic networks

AU - Inoue, Masaki

AU - Imura, Jun Ichi

AU - Kashima, Kenji

AU - Suzuki, Masayasu

AU - Aihara, Kazuyuki

PY - 2015/12/1

Y1 - 2015/12/1

N2 - 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.

AB - 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.

KW - absolute instability

KW - biological systems

KW - Lur'e systems

KW - uncertain systems

UR - http://www.scopus.com/inward/record.url?scp=84955210891&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84955210891&partnerID=8YFLogxK

U2 - 10.1002/rnc.3294

DO - 10.1002/rnc.3294

M3 - Article

VL - 25

SP - 3746

EP - 3762

JO - International Journal of Robust and Nonlinear Control

JF - International Journal of Robust and Nonlinear Control

SN - 1049-8923

IS - 18

ER -