Stability Analysis of Three-Agent Consensus Dynamics With Fixed Topology and Three Non-Identical Delays

In this paper, we consider a strongly connected three-agent consensus dynamics with three non-identical communication delays, where each delay arises between a pair of agents. Asymptotic stability of consensus mission is of question in presence of delays, and to study this we propose a new and computationally efficient technique that detects stability transitions with respect to delays. This new technique originates from frequency sweeping ideas and ultimately leads to stability robustness maps of the system with respect to three delays. Proofs related to the analysis are sketched. A case study is provided to demonstrate the effectiveness of the approach and the trade-off between controller gains versus delays.