Weighted Averaged Behavior of Synchronization among Heterogeneous Agents in a Sampled-data Setting

In this paper, we address the problem of synchronization among heterogeneous agents in a sampled-data setting. The key observation is that the sample-and-hold process introduces additional node-wise weights on the Laplacian matrix in the discrete-time domain. We then show that in the sampled-data setting, all of the agents' states approach the state of the so-called weighted averaged dynamics, an auxiliary dynamics that represents the collective behavior of heterogeneous agents when they are synchronized. In addition, admissible ranges of the sampling period and the diffusive coupling gain are computed, with which the consensus among the agents is achieved in a practical sense.