A Study Of The Fixed-time Bipartite Consensus Of Multi-agent System With Disturbances

In recent years,due to the fast development of multi-agent,as well as the increasing requirements for actual needs to the system,a large number of researchers have made in further research on the related problems of multi-agent system.the problem of how to achieve a stable state in a fixed time has become an important research direction,in which the fixed time stability algorithm is an indispensable part.In this paper,we mainly study the fixed time bipartite consensus problem of multi-agent system under the condition of disturbance.On the one hand,based on algebraic graph theory and fixed-time stability theorem,a new control protocol is proposed to solve the multi-agent system with disturbances realize fixed-time bipartite consensus,and the upper bound of convergence time for multi-agent system realize bipartite consensus at fixed time is given.Finally,the feasibility of the proposed protocol is proved by Matlab simulation.On the other hand,we discussed the fixed-time asymmetric bipartite consensus of multi-agent system with disturbances.Based on algebraic graph theory and fixed-time stability theorem,a new control protocol is proposed,and the generalized Laplacian matrix is used to make the multi-agent system with disturbances can realize fixed-time asymmetric bipartite consensus,and the upper bound of convergence time for multi-agent system realize asymmetric bipartite consensus at fixed time is given.Finally,the validity of the proposed protocol is verified by Matlab simulation.