Fully distributed consensus for general linear multi-agent systems with unknown external disturbances

This study investigates the consensus problem for general linear multi-agent systems with unknown external disturbances. Both the leaderless and the leader-follower consensus problems are considered. By using the absolute output information of each agent, the local states and external disturbances of each agent can be estimated by an extended state observer. Then, by using the relative estimated states and disturbance estimation, the continuous controller can be designed in a fully distributed fashion, which ensures that the consensus error of general linear multi-agent systems converges to zero eventually with the complete disturbance rejection. Moreover, when the absolute output information of each agent is not available, it is shown that the consensus problem can be solved by using only relative output information of neighbouring agents but only the part of the disturbances that affect the common trajectories will be rejected. Finally, simulation examples are given to demonstrate the effectiveness of the proposed protocols. Compared with the previous related works, fully distributed consensus disturbance rejection protocols are developed based on node-based adaptive design and edge-based adaptive design, which require neither global information of the communication graph nor the prior knowledge of the disturbance model.