On the robust synchronization of Brockett oscillators

Hafiz Ahmed, Rosane Ushirobira, Denis Efimov

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
16 Downloads (Pure)


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
Issue number14
Publication statusPublished - 9 Aug 2016


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


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