Robust bifurcation analysis based on the Nyquist stability criterion

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

doi:10.1109/CDC.2013.6760138

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 proceeding › Conference contribution

8 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 language	English
Title of host publication	2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1768-1773
Number of pages	6
ISBN (Print)	9781467357173
DOIs	https://doi.org/10.1109/CDC.2013.6760138
Publication status	Published - 2013
Externally published	Yes
Event	52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy Duration: 2013 Dec 10 → 2013 Dec 13

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	52nd IEEE Conference on Decision and Control, CDC 2013
Country/Territory	Italy
City	Florence
Period	13/12/10 → 13/12/13

ASJC Scopus subject areas

Control and Systems Engineering
Modelling and Simulation
Control and Optimization

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10.1109/CDC.2013.6760138

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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

Robust bifurcation analysis based on the Nyquist stability criterion. / Inoue, Masaki; Imura, Jun Ichi; Kashima, Kenji et al.
2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013. Institute of Electrical and Electronics Engineers Inc., 2013. p. 1768-1773 6760138 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Inoue, M, Imura, JI, 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., 6760138, Proceedings of the IEEE Conference on Decision and Control, 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

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AB - 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.

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Robust bifurcation analysis based on the Nyquist stability criterion

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