Cluster-bipartite consensus control for singular multi-agent systems under cooperative–competitive networks

This paper investigates the distributed cluster-bipartite state consensus control problem for leader-following linear singular multi-agent systems (MASs) under cooperative–competitive networks. A new cluster-bipartite consensus framework incorporating singular dynamics and multiple leaders is established. First, by introducing a neighbouring consensus error with a sign function, a distributed state feedback controller is proposed based on the generalised algebraic Riccati inequality. When the directed signed graph of each subgroup satisfies the structural balance condition, all followers within any cluster can achieve bipartite state tracking within two opposing subgroups. Second, for scenarios where system states are unavailable, an output feedback controller based on distributed state observers is further designed. Moreover, the proposed distributed control protocols are extended to solve the cluster-bipartite formation control problem. Finally, numerical simulation examples are provided to demonstrate the effectiveness of the proposed algorithms.