Delay Margins for Average Consensus Problems Using Partial Difference Equation Analysis

In this paper, we revisit average consensus problems for undirected networks of agents subject to communication delays and switching topologies within the framework of partial difference equations over graphs. Focusing on integrator-type agents, we primarily study tight estimates of the maximal tolerable delay for an observer-type protocol. This protocol, a variant of the delayed Laplacian, is designed to enhance disturbance rejection. Uniform/nonuniform delays associated with static/switching topologies are handled in a unified framework. The main results provide scalable and computationally simple sufficient conditions for average consensus, which are also shown to be necessary in certain cases. Compared to the state of the art, the proposed method not only recovers known delay upper bounds but also achieves tighter bounds in several scenarios.