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

Journal article (2018)

Authors

Libo Su Katholieke Universiteit Leuven
Yanling Wei Katholieke Universiteit Leuven
Wim Michiels Katholieke Universiteit Leuven
E. Steur Team Bart De Schutter - Mechanical, Maritime and Materials Engineering
Henk Nijmeijer Eindhoven University of Technology
Research Group
Team Bart De Schutter (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2018 Libo Su, Yanling Wei, Wim Michiels, E. Steur, Henk Nijmeijer
DOI: https://doi.org/10.1016/j.ifacol.2018.12.094
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Published Date

2018

Language

English

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Bart De Schutter

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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