Consensus of Multi-agent Systems Based on Distributed PI And PD Control Protocol Over Directed Topology

In the paper, the consensus problem of the first-order multi-agent systems with time-delay is investigated. The communication topology of the multi-agent systems is assumed to be directed and has a directed spanning tree. Firstly, the consensus problem of the multi-agent systems is transformed into the stability problem of the error systems by using special matrix. Then, the distributed PI-like and PD-like control protocols are designed to guarantee the agents can reach stability asymptotically. Sufficient conditions which can be easily derived by constructing a suitable Lyapunov-Krasovskii functional. Finally, numerical simulations demonstrated the correctness and effectiveness of the obtained theorems.