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 publicationProceedings of the IEEE Conference on Decision and Control
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1768-1773
Number of pages6
ISBN (Print)9781467357173
DOIs
Publication statusPublished - 2013
Externally publishedYes
Event52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy
Duration: 2013 Dec 102013 Dec 13

Other

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

Fingerprint

Stability criteria
Bifurcation Analysis
Stability Criteria
Hyperbolicity
Uncertainty
Pole
Poles
Norm-bounded Uncertainties
Uncertain Systems
Linear systems
Bifurcation
Genes
Unstable
Linear Systems
Robustness
Gene
Necessary Conditions
Dependent
Sufficient Conditions

ASJC Scopus subject areas

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

Cite this

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

Robust bifurcation analysis based on the Nyquist stability criterion. / Inoue, Masaki; Imura, Jun Ichi; Kashima, Kenji; Aihara, Kazuyuki.

Proceedings of the IEEE Conference on Decision and Control. Institute of Electrical and Electronics Engineers Inc., 2013. p. 1768-1773 6760138.

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

Inoue, M, Imura, JI, Kashima, K & Aihara, K 2013, Robust bifurcation analysis based on the Nyquist stability criterion. in Proceedings of the IEEE Conference on Decision and Control., 6760138, Institute of Electrical and Electronics Engineers Inc., pp. 1768-1773, 52nd IEEE Conference on Decision and Control, CDC 2013, Florence, Italy, 13/12/10. https://doi.org/10.1109/CDC.2013.6760138
Inoue M, Imura JI, Kashima K, Aihara K. Robust bifurcation analysis based on the Nyquist stability criterion. In Proceedings of the IEEE Conference on Decision and Control. Institute of Electrical and Electronics Engineers Inc. 2013. p. 1768-1773. 6760138 https://doi.org/10.1109/CDC.2013.6760138
Inoue, Masaki ; Imura, Jun Ichi ; Kashima, Kenji ; Aihara, Kazuyuki. / Robust bifurcation analysis based on the Nyquist stability criterion. Proceedings of the IEEE Conference on Decision and Control. Institute of Electrical and Electronics Engineers Inc., 2013. pp. 1768-1773
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