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

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

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Abstract

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
JournalIFAC-PapersOnLine
Volume51
Issue number33
DOIs
Publication statusPublished - 2018
EventCHAOS 2018: 5th IFAC Conference on Analysis and Control of Chaotic Systems - Eindhoven, Netherlands
Duration: 30 Oct 20181 Nov 2018

Keywords

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

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