Bipartite Fixed-time Output Consensus of Singular Heterogeneous Linear Multi-agent Systems Under Directed Signed Topology

This research investigates bipartite fixed-time output consensus of singular heterogeneous linear multi-agent systems (SHL-MASs) under directed signed topology, and both fixed and switching topologies are considered. Firstly, a bipartite fixed-time observer of leader under fixed directed signed graph is proposed. The estimates have the same modulus with the leader’s state but may differ in sign due to the coexistence of cooperative and antagonistic interactions. Then, it is extended to switching directed signed topology case. Next, fixed-time control law is designed for a reduced-order normal heterogeneous linear MASs, which can equivalently solve the bipartite fixed-time output consensus problem of SHL-MASs. Finally, examples are given to demonstrate the results.