🤖 AI Summary
This paper investigates diffusion-type consensus in multi-dimensional networks featuring both intra-layer and inter-layer time delays, under uniform interaction patterns across layers. To address analytical challenges arising from the coupling between time delays and network topology, we propose, for the first time, a unified “structure–interaction pattern–delay” joint modeling framework that systematically captures the synergistic effects of inter-layer coupling and time delays under repeated interactions. Leveraging eigenvalue analysis and Lyapunov stability theory, we derive an explicit, computationally tractable sufficient condition for global asymptotic consensus, parameterized by the network topology, local coupling matrices, and the upper bound of time delays. Numerical simulations validate the effectiveness and practicality of the criterion. The proposed framework provides an interpretable, analytically grounded theoretical tool for consensus analysis in delayed multi-dimensional networks.
📝 Abstract
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.