Bipartite Fixed-Time Output Consensus of Heterogeneous Linear Multiagent Systems

In this article, the bipartite fixed-time output consensus problem of heterogeneous linear multiagent systems (MASs) is investigated. First, a distributed bipartite fixed-time observer is proposed, by which the follower can estimate the leader's state. The estimate value is the same as the leader's state in modulus but may not in sign due to the existence of antagonistic interactions between agents. Then, an adaptive bipartite fixed-time observer is further proposed. It is fully distributed without involving any global information. This adaptive bipartite fixed-time observer can estimate not only the leader's system matrix but also the leader's state. Next, distributed nonlinear control laws are developed based on two observers, respectively, such that the bipartite fixed-time output consensus of heterogeneous linear MASs can be achieved. Moreover, the upper bound of the settling time is independent of initial states of agents. Finally, the examples are given to demonstrate the results.