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.
|Publication status||Published - 2018|
|Event||CHAOS 2018: 5th IFAC Conference on Analysis and Control of Chaotic Systems - Eindhoven, Netherlands|
Duration: 30 Oct 2018 → 1 Nov 2018
- linear matrix inequalities
- linear parameter-varying systems
- Partial synchronization
- time-delay systems