Robust bifurcation analysis based on the Nyquist stability criterion

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Citations (Scopus)

Abstract

In this paper, we propose a novel method for robust bifurcation analysis of systems with dynamic uncertainties. First, we formulate a robust bifurcation analysis problem for parameter-dependent systems with norm-bounded uncertainties. Next, to solve this problem, we define a new concept of robust hyperbolicity of an equilibrium that for any uncertainty an uncertain linear system has no neutral pole and the number of unstable poles is constant. A necessary and sufficient condition for the robust hyperbolicity is derived from the Nyquist stability criterion. On the basis of the condition, we propose a method for identifying the region that consists of all potential bifurcation boundaries. Finally, robustness of a gene-metabolic oscillator with dynamic uncertainties is investigated by using the proposed method.

Original languageEnglish
Title of host publication2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1768-1773
Number of pages6
ISBN (Print)9781467357173
DOIs
Publication statusPublished - 2013 Jan 1
Externally publishedYes
Event52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy
Duration: 2013 Dec 102013 Dec 13

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other52nd IEEE Conference on Decision and Control, CDC 2013
CountryItaly
CityFlorence
Period13/12/1013/12/13

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

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  • Cite this

    Inoue, M., Imura, J. I., Kashima, K., & Aihara, K. (2013). Robust bifurcation analysis based on the Nyquist stability criterion. In 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013 (pp. 1768-1773). [6760138] (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2013.6760138