A Lyapunov approach to stability analysis of partial synchronization in delay-coupled networks

Libo Su, Yanling Wei, Wim Michiels, Erik Steur, Henk Nijmeijer

Research output: Contribution to journalConference articlepeer-review


Networks of interconnected dynamical systems may exhibit a so-called partial synchronization phenomenon, which refers to synchronous behaviors of some but not all of the systems. The patterns of partial synchronization are often characterized by partial synchronization manifolds, which are linear invariant subspace of the state space of the network dynamics. Here, we propose a Lyapunov-Krasovskii approach to analyze the stability of partial synchronization manifolds in delay-coupled networks. First, the synchronization error dynamics are isolated from the network dynamics in a systematic way. Second, we use a parameter-dependent Lyapunov-Krasovskii functional to assess the local stability of the manifold, by employing techniques originally developed for linear parameter-varying (LPV) time-delay systems. The stability conditions are formulated in the form of linear matrix inequalities (LMIs) which can be solved by several available tools.
Original languageEnglish
Pages (from-to)198-204
Number of pages7
Issue number33
Publication statusPublished - 2018


  • Partial synchronization
  • linear parameter-varying systems
  • time-delay systems
  • linear matrix inequalities

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