Consensus seeking in diffusive multidimensional networks with a repeated interaction pattern and time-delays

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.