Exact Prescribed-time Average Consensus Using Periodic Delay Feedback

Current prescribed-time methods typically achieve only inexact consensus with residual errors, as they deliberately circumvent the singularity issues inherent in high-gain approaches. This paper revisits the prescribed-time consensus problem for multi-agent systems and proposes a solution via a novel periodic time-delay feedback protocol. The protocol guarantees exact consensus (zero error) within at most two delay periods. To establish theoretical validity, we introduce a novel Lyapunov-based criterion tailored for delayed systems. Crucially, this work completely circumvents the singularity problem - a limitation that renders existing approaches impractical. Finally, numerical simulations implement the prescribed-time formation control using the proposed protocol, further validating its theoretical effectiveness.