Synchronization of Coupled Harmonic Oscillators by Time-Dependent Topology Switching

This paper studies the approach of taking network topology as a control variable for the analysis of coupled harmonic oscillators. We particularly consider the setting where the local control inputs of individual oscillators are governed by their relative positions. Based on the known results in the theory of stability of switched linear systems, we propose a time-dependent topology-switching algorithm that enables the oscillators to asymptotically achieve synchronization. The main advantages of the proposed method, with respect to the prior work, are two-fold: we allow the coupling strength to be negative; and we do not constrain the magnitude of positive coupling strength. Simulation results are provided to verify the effectiveness of the algorithm.