A synchronization condition for coupled nonlinear systems with time-delay: A frequency domain approach

Toshiki Oguchi, Henk Nijmeijer

Research output: Contribution to journalArticleAcademicpeer-review

14 Citations (Scopus)

Abstract

This paper considers the synchronization problem for nonlinear systems with time-delay couplings. We assume that the error dynamics can be rewritten as a feedback connection of a linear delay system with multiple inputs and outputs and nonlinear elements which are decentralized and satisfy a sector condition. Then, we derive a synchronization condition for time-delay coupled systems by applying the multivariable circle criterion. Unlike the conventional synchronization criteria, the derived criterion is based on a frequency-domain stability condition and avoids the use of the Lyapunov Krasovskii approach. As a result, the condition based on the circle criterion does not contain the conservativeness caused by the LyapunovKrasovskii approach. The effectiveness of the proposed criterion is shown by examples of coupled Chua systems with delay coupling.

Original languageEnglish
Pages (from-to)2525-2538
Number of pages14
JournalInternational Journal of Bifurcation and Chaos : in Applied Sciences and Engineering
Volume21
Issue number9
DOIs
Publication statusPublished - Sept 2011

Bibliographical note

Funding Information:
This work was partially supported by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (No. 20560424).

Keywords

  • Absolute stability
  • Chaos synchronization
  • Circle criterion
  • Time-delay

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