A Lyapunov approach to stability analysis of partial synchronization in delay-coupled networks ⁎. Issue 33 (2018)

• Record Type: Journal Article
• Authors: Su, Libo; Wei, Yanling; Michiels, Wim; Steur, Erik; Nijmeijer, Henk
• Is Part Of: IFAC-PapersOnLine. Volume 51:Issue 33(2018)
• Page Start: 198
• Page End: 204
• Publication Date: 2018
• Subjects: Partial synchronization -- linear parameter-varying systems -- time-delay systems -- linear matrix inequalities; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2018.12.094
• Languages: English
• ISSNs: 2405-8963

Abstract

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.