Delay robustness in consensus problems

We investigate the robustness of consensus schemes for linear Multi-Agent Systems (MAS) to feedback delays. To achieve this, we develop a unified framework that considers linear MAS models with different feedback delays, e.g. affecting only the neighbor’s output, or affecting both the agent’s own and its neighbors’ output. This framework has the advantage of providing scalable, simple, and accurate set-valued conditions for consensus. Using these set-valued conditions, previous results on consensus in MAS with delays can be recovered and generalized. Moreover, we use them to derive conditions for the convergence rate of single integrator MAS with feedback delays. Finally, building on this framework, we propose a scalable delay-dependent design algorithm for consensus controllers for a large class of linear MAS.