The Leader-follower Two-way Convergence Of The Controller Is Triggered Based On The Event

This paper considers bipartite consensus of leader-follower multi-agent systems.As is known,the event-triggered controller has the advantages of low update frequency and low communication cost.By introducing a time-varying gain function,event-triggered controllers are designed for single-integrator followers in the presence/absence of measure-ment noise.By using tools from algebraic graph theory,matrix analysis and stochastic analysis theory,communication topology condition and gain condition are given to ensure the leader-follower bipartite consensus based on the proposed event-triggered controllers.Moreover,these conditions are proved to be necessary and sufficient.It is found that the signed digraph being structurally balanced and having a spanning tree are not only sufficient but also necessary conditions for achieving leader-follower bipartite consensus regardless of the measurement noise.