Abstract: The observer-based H_∞-consensus control problem is studied for multi-agent systems with nonlinear dynamics under the Round-Robin (RR) communication protocol. The Round-Robin protocol is implemented in the communication channels from one agent to the neighboring agents to alleviate the measurement loss, delay and other problems caused by channel congestions so that the agent can only receive the information from one neighbor agent at each time instant. First, the state observers are designed based on the measurement outputs to estimate the states of the agents. Then, consensus controllers are designed based on the estimates from the observers. By resorting to the Lyapunov stability theory, sufficient conditions are given such that the H_∞-consensus performance index is guaranteed. The parameters of the observers and the controllers are then characterized by solving certain matrix inequalities. Finally, the proposed control algorithm is applied to numerical simulation and consensus control of the flexible link robot to verify the feasibility and effectiveness of the designed algorithm.