Abstract:This paper investigates the robustness problem for consensus and cooperative control of the first order multi-agent systems with multi-graph communication affected by external disturbance. Robustness is quantified as the ??2 norm of the closed-loop system. The direct relationship among robustness of consensus, system ??2 norm, system communication topology for the oriented multi-agent systems are constructed when there exists self-loops or not in the communication topology in this note, which is based on the graph theory, the control theory and the matrix theory, and the rigorous proof is given in details. When the communication topology is complete graph, star graph, path graph and cycle graph, the convergence speed and robustness are analyzed and compared among them. Simulation examples are given to illustrate the effectiveness of the proposed methed.