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

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

Su, Libo (Katholieke Universiteit Leuven)
Wei, Yanling (Katholieke Universiteit Leuven)
Michiels, Wim (Katholieke Universiteit Leuven)
Steur, E. (TU Delft Team Bart De Schutter)
Nijmeijer, Henk (Eindhoven University of Technology)

2018

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.

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

http://resolver.tudelft.nl/uuid:280f66c1-91ad-45ec-b2f3-bc0775c0d742

https://doi.org/10.1016/j.ifacol.2018.12.094

2405-8963

IFAC-PapersOnLine, 51 (33), 198-204

CHAOS 2018: 5th IFAC Conference on Analysis and Control of Chaotic Systems, 2018-10-30 → 2018-11-01, Eindhoven, Netherlands

Institutional Repository

journal article

© 2018 Libo Su, Yanling Wei, Wim Michiels, E. Steur, Henk Nijmeijer