This paper studies a consensus problem in multidimensional networks having the same agent-to-agent interaction pattern under both intra- and cross-layer time delays. Several conditions for the agents to globally asymptotically achieve a consensus are derived, which involve the overall network's structure, the local interacting pattern, and the values of the time delays. The validity of these conditions is proved by direct eigenvalue evaluation and supported by numerical simulations.

翻译：本文研究了具有相同节点间交互模式的多维网络在层内和跨层时滞下的共识问题。推导了使网络全局渐近达成共识的若干条件，这些条件涉及整体网络结构、局部交互模式及时滞值。通过直接特征值评估验证了上述条件的有效性，并通过数值仿真予以支持。