Observer-based prescribed-time lag bipartite consensus of nonlinear multi-agent systems under event-triggered mechanism

Considering the complexity of lag time and the convergence time, as well as the influence of the observer and the event-triggered mechanism, the prescribed-time lag bipartite consensus (PTLBC) control problem for nonlinear multi-agent systems (MASs) is researched in the paper. First of all, it designs the prescribed-time dynamic observer (PTDO) for followers to get the states of the leader within an arbitrarily prescribed time. Furthermore, to significantly decrease the communication consumption, the innovative event-triggered mechanism is studied for followers. To realize the lag bipartite consensus (LBC) of nonlinear MASs within an arbitrarily prescribed time, a PTLBC control scheme is presented via the aforementioned PTDO and event-triggered mechanism. With Lyapunov stability analysis method, sufficient conditions are obtained and detailed stability analysis is studied, which indicates that the nonlinear MASs can realize PTLBC. Furthermore, the analysis proves that the proposed event-triggered mechanism excludes Zeno behaviour. The theoretical analysis is validated by means of a simulation example.