Group‐bipartite consensus for heterogeneous multi‐agent systems with general linear dynamics

The group‐bipartite consensus problem for linear multi‐agent systems (MASs) is examined. The network topology studied in this paper is directed and has no acyclic constraints. For a network with both cooperative and competitive interactions within each group, a novel in‐degree balanced condition is proposed to balance mutual influence among different groups. A distributed control protocol is proposed for leaderless linear MASs to achieve group‐bipartite consensus. Moreover, a distributed control protocol is also proposed for leader‐following linear MASs by using a pinning control strategy. Sufficient conditions for the control protocol's feasibility are derived using Lyapunov stability theory. Finally, numerical simulations confirm the proposed protocol's feasibility.