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 articleAcademicpeer-review

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.
LanguageEnglish
Pages198-204
Number of pages7
JournalIFAC-PapersOnLine
Volume51
Issue number33
DOIs
StatePublished - 2018

Keywords

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

Cite this

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title = "A Lyapunov approach to stability analysis of partial synchronization in delay-coupled networks",
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.",
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A Lyapunov approach to stability analysis of partial synchronization in delay-coupled networks. / Su, Libo; Wei, Yanling; Michiels, Wim; Steur, Erik; Nijmeijer, Henk.

In: IFAC-PapersOnLine, Vol. 51, No. 33, 2018, p. 198-204.

Research output: Contribution to journalConference articleAcademicpeer-review

TY - JOUR

T1 - A Lyapunov approach to stability analysis of partial synchronization in delay-coupled networks

AU - Su,Libo

AU - Wei,Yanling

AU - Michiels,Wim

AU - Steur,Erik

AU - Nijmeijer,Henk

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Partial synchronization

KW - linear parameter-varying systems

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KW - linear matrix inequalities

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