Robust bifurcation analysis of systems with dynamic uncertainties

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

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this paper, we propose in uncertain dynamical systems a novel method for identifying the region that includes all possible bifurcation boundaries. First, we formulate a robust bifurcation analysis problem for parameter-dependent differential equations with dynamic uncertainties. Next, to solve this problem, we give stability and instability conditions for the uncertain system. Finally, on the basis of these conditions, we propose a method for solving the robust bifurcation analysis problem.

Original languageEnglish
Article number1350157
JournalInternational Journal of Bifurcation and Chaos
Volume23
Issue number9
DOIs
Publication statusPublished - 2013 Sep
Externally publishedYes

Fingerprint

Bifurcation Analysis
Uncertainty
Bifurcation (mathematics)
Uncertain systems
Dynamical systems
Differential equations
Uncertain Systems
Bifurcation
Dynamical system
Differential equation
Dependent

Keywords

  • Bifurcation theory
  • feedback control theory
  • robust control theory

ASJC Scopus subject areas

  • Applied Mathematics
  • General
  • Engineering(all)
  • Modelling and Simulation

Cite this

Robust bifurcation analysis of systems with dynamic uncertainties. / Inoue, Masaki; Imura, Jun Ichi; Kashima, Kenji; Aihara, Kazuyuki.

In: International Journal of Bifurcation and Chaos, Vol. 23, No. 9, 1350157, 09.2013.

Research output: Contribution to journalArticle

Inoue, Masaki ; Imura, Jun Ichi ; Kashima, Kenji ; Aihara, Kazuyuki. / Robust bifurcation analysis of systems with dynamic uncertainties. In: International Journal of Bifurcation and Chaos. 2013 ; Vol. 23, No. 9.
@article{0ee862e9fc4e4ac2886fdae3d509f679,
title = "Robust bifurcation analysis of systems with dynamic uncertainties",
abstract = "In this paper, we propose in uncertain dynamical systems a novel method for identifying the region that includes all possible bifurcation boundaries. First, we formulate a robust bifurcation analysis problem for parameter-dependent differential equations with dynamic uncertainties. Next, to solve this problem, we give stability and instability conditions for the uncertain system. Finally, on the basis of these conditions, we propose a method for solving the robust bifurcation analysis problem.",
keywords = "Bifurcation theory, feedback control theory, robust control theory",
author = "Masaki Inoue and Imura, {Jun Ichi} and Kenji Kashima and Kazuyuki Aihara",
year = "2013",
month = "9",
doi = "10.1142/S0218127413501575",
language = "English",
volume = "23",
journal = "International Journal of Bifurcation and Chaos",
issn = "0218-1274",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "9",

}

TY - JOUR

T1 - Robust bifurcation analysis of systems with dynamic uncertainties

AU - Inoue, Masaki

AU - Imura, Jun Ichi

AU - Kashima, Kenji

AU - Aihara, Kazuyuki

PY - 2013/9

Y1 - 2013/9

N2 - In this paper, we propose in uncertain dynamical systems a novel method for identifying the region that includes all possible bifurcation boundaries. First, we formulate a robust bifurcation analysis problem for parameter-dependent differential equations with dynamic uncertainties. Next, to solve this problem, we give stability and instability conditions for the uncertain system. Finally, on the basis of these conditions, we propose a method for solving the robust bifurcation analysis problem.

AB - In this paper, we propose in uncertain dynamical systems a novel method for identifying the region that includes all possible bifurcation boundaries. First, we formulate a robust bifurcation analysis problem for parameter-dependent differential equations with dynamic uncertainties. Next, to solve this problem, we give stability and instability conditions for the uncertain system. Finally, on the basis of these conditions, we propose a method for solving the robust bifurcation analysis problem.

KW - Bifurcation theory

KW - feedback control theory

KW - robust control theory

UR - http://www.scopus.com/inward/record.url?scp=84885824008&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84885824008&partnerID=8YFLogxK

U2 - 10.1142/S0218127413501575

DO - 10.1142/S0218127413501575

M3 - Article

AN - SCOPUS:84885824008

VL - 23

JO - International Journal of Bifurcation and Chaos

JF - International Journal of Bifurcation and Chaos

SN - 0218-1274

IS - 9

M1 - 1350157

ER -