Leader–Follower Bipartite Consensus of Linear Multiagent Systems Over a Signed Directed Graph

In this brief, leader-follower bipartite consensus of a group of linear multiagent systems is studied over a signed directed graph where all the followers are subjected to mismatched unknown bounded disturbances. To that end, a distributed extended state observer where the disturbances are the extended state and a distributed relative output feedback consensus control law are designed to achieve bipartite consensus. With the suitable design of scaler coupling gain parameters, and feedback gain and observer gain matrices obtained from linear matrix inequalities, it is shown that if the signed directed graph contains a directed spanning tree rooted at the leader node, then the designed consensus protocol simultaneously stabilizes both the bipartite consensus error and observer estimation error with the errors converging to a small bounded set. The simulation results verify the effectiveness of the proposed method.