Some Results on Exponential Synchronization of Nonlinear Systems

Vincent Andrieu*, Bayu Jayawardhana, Sophie Tarbouriech

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

5 Citations (Scopus)


Based on recent works on transverse exponential stability, we establish some necessary and sufficient conditions for the existence of a (locally) exponential synchronizing control law. We show that the existence of a structured synchronizer is equivalent to the existence of a stabilizer for the individual linearized systems (on the synchronization manifold) by a linear state feedback. This, in turn, is also equivalent to the existence of a symmetric covariant tensor field, which satisfies a control matrix function inequality. Based on this result, we provide the construction of such a synchronizer via backstepping approach. In some particular cases, we show how global exponential synchronization may be obtained.

Original languageEnglish
Pages (from-to)1213-1219
Number of pages7
JournalIEEE Transactions on Automatic Control
Issue number4
Early online date3-Jan-2018
Publication statusPublished - Apr-2018


  • Lyapunov stability
  • multi-agent systems
  • synchronization
  • lyapunov methods

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