Complete synchronization for a second-order Kuramoto type model of identical oscillators in a switching network

In this paper, we investigate the interplay of inertia and a switching network on synchronization of an ensemble of identical Kuramoto oscillators. Under some conditions on initial data and model parameters, we provide a sufficient framework for phase-frequency synchronization. Moreover, we show that the system achieves a synchronous state at an exponential rate. The analysis in this paper is based on matrix analysis. We extend a critical property owned by a connected stochastic matrix, which plays an important role in our proof.