On the robust synchronization of Brockett oscillators

Hafiz Ahmed, Rosane Ushirobira, Denis Efimov

Research output: Contribution to journalArticle

3 Citations (Scopus)
6 Downloads (Pure)

Abstract

In this article, motivated by a recent work of R. Brockett Brockett (2013), we study a robust synchronization problem for multistable Brockett oscillators within an Input-to-State Stability (ISS) framework. Based on a recent generalization of the classical ISS theory to multistable systems and its application to the synchronization of multistable systems, a synchronization protocol is designed with respect to compact invariant sets of the unperturbed Brockett oscillator. The invariant sets are assumed to admit a decomposition without cycles (i.e. with neither homoclinic nor heteroclinic orbits). Contrarily to the local analysis of Brockett (2013), the conditions obtained in our work are global and applicable for family of non-identical oscillators. Numerical simulation examples illustrate our theoretical results.
Original languageEnglish
Pages (from-to)142-147
Number of pages6
JournalIFAC-PapersOnLine
Volume49
Issue number14
DOIs
Publication statusPublished - 9 Aug 2016

Fingerprint

Synchronization
Orbits
Decomposition
Computer simulation

Keywords

  • Input-to-State Stability
  • Synchronization
  • Multistability
  • Brockett oscillator

Cite this

On the robust synchronization of Brockett oscillators. / Ahmed, Hafiz; Ushirobira, Rosane; Efimov, Denis .

In: IFAC-PapersOnLine, Vol. 49, No. 14, 09.08.2016, p. 142-147.

Research output: Contribution to journalArticle

Ahmed, Hafiz ; Ushirobira, Rosane ; Efimov, Denis . / On the robust synchronization of Brockett oscillators. In: IFAC-PapersOnLine. 2016 ; Vol. 49, No. 14. pp. 142-147.
@article{6f2f2a7420c74d0699a9787a0475631f,
title = "On the robust synchronization of Brockett oscillators",
abstract = "In this article, motivated by a recent work of R. Brockett Brockett (2013), we study a robust synchronization problem for multistable Brockett oscillators within an Input-to-State Stability (ISS) framework. Based on a recent generalization of the classical ISS theory to multistable systems and its application to the synchronization of multistable systems, a synchronization protocol is designed with respect to compact invariant sets of the unperturbed Brockett oscillator. The invariant sets are assumed to admit a decomposition without cycles (i.e. with neither homoclinic nor heteroclinic orbits). Contrarily to the local analysis of Brockett (2013), the conditions obtained in our work are global and applicable for family of non-identical oscillators. Numerical simulation examples illustrate our theoretical results.",
keywords = "Input-to-State Stability, Synchronization, Multistability, Brockett oscillator",
author = "Hafiz Ahmed and Rosane Ushirobira and Denis Efimov",
year = "2016",
month = "8",
day = "9",
doi = "10.1016/j.ifacol.2016.07.999",
language = "English",
volume = "49",
pages = "142--147",
journal = "IFAC-PapersOnLine",
issn = "2405-8963",
publisher = "IFAC Secretariat",
number = "14",

}

TY - JOUR

T1 - On the robust synchronization of Brockett oscillators

AU - Ahmed, Hafiz

AU - Ushirobira, Rosane

AU - Efimov, Denis

PY - 2016/8/9

Y1 - 2016/8/9

N2 - In this article, motivated by a recent work of R. Brockett Brockett (2013), we study a robust synchronization problem for multistable Brockett oscillators within an Input-to-State Stability (ISS) framework. Based on a recent generalization of the classical ISS theory to multistable systems and its application to the synchronization of multistable systems, a synchronization protocol is designed with respect to compact invariant sets of the unperturbed Brockett oscillator. The invariant sets are assumed to admit a decomposition without cycles (i.e. with neither homoclinic nor heteroclinic orbits). Contrarily to the local analysis of Brockett (2013), the conditions obtained in our work are global and applicable for family of non-identical oscillators. Numerical simulation examples illustrate our theoretical results.

AB - In this article, motivated by a recent work of R. Brockett Brockett (2013), we study a robust synchronization problem for multistable Brockett oscillators within an Input-to-State Stability (ISS) framework. Based on a recent generalization of the classical ISS theory to multistable systems and its application to the synchronization of multistable systems, a synchronization protocol is designed with respect to compact invariant sets of the unperturbed Brockett oscillator. The invariant sets are assumed to admit a decomposition without cycles (i.e. with neither homoclinic nor heteroclinic orbits). Contrarily to the local analysis of Brockett (2013), the conditions obtained in our work are global and applicable for family of non-identical oscillators. Numerical simulation examples illustrate our theoretical results.

KW - Input-to-State Stability

KW - Synchronization

KW - Multistability

KW - Brockett oscillator

U2 - 10.1016/j.ifacol.2016.07.999

DO - 10.1016/j.ifacol.2016.07.999

M3 - Article

VL - 49

SP - 142

EP - 147

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

SN - 2405-8963

IS - 14

ER -