Fast Consensus of Discrete Multi-Agent Systems with Delay

This paper studied the fast consensus of discrete multi-agent systems (MASs) with time delay. A consensus protocol incorporating memory information is formulated to accelerate consensus. The necessary and sufficient conditions to reach average consensus are provided. Furthermore, an optimal design of the fast consensus for MASs with small delay is given, and the explicit solutions of the fastest convergence speed and corresponding optimal control gains are deduced. Finally, the theoretical findings are validated through numerical simulations, underscoring the effectiveness of the nronosed annroach.