Synchronization of linear oscillators coupled through a dynamic network with interior nodes

The research article “Synchronization of linear oscillators coupled through a dynamic network with interior nodes”, authored by METU member Assoc. Prof. Sezai Emre Tuna, has been published in Automatica.

Synchronization is studied in an array of identical linear oscillators of arbitrary order, coupled through a dynamic network comprising dissipative connectors (e.g., dampers) and restorative connectors (e.g., springs). The coupling network is allowed to contain interior nodes, i.e., those that are not directly connected to an oscillator. It is shown that the oscillators asymptotically synchronize if and only if the Schur complement (with respect to the boundary nodes) of the complex-valued Laplacian matrix representing the coupling has a single eigenvalue on the imaginary axis.

Tuna, S. E. (2020). Synchronization of linear oscillators coupled through a dynamic network with interior nodes. Automatica, 117 doi:10.1016/j.automatica.2020.109008

Article access: https://www.sciencedirect.com/science/article/pii/S0005109820302065?via%3Dihub

Keywords:

Interior node; Linear oscillator; Schur complement; Synchronization