Bipartite Consensus Of Multi-agent Systems Based On Reduced-order Observer

For multi-agent systems,its collaborative control has become a hot topic,and it has been widely used in transportation,engineering,military and other aspects.The consensus problem is the core of the collaborative control problem,and the bipartite consensus problem extended by it is becoming more and more popular.Although some scholars have discussed the bipartite consensus problem,few people study it based on reduced-order observers.Considering the practical applicability,this paper discusses the bipartite consensus as follows:For general linear multi-agent systems,this paper considers that the output information contains part of the state information.To remove excessiveness and cut down the workload,a reduced-order observer is constructed by using Sylvester equations.Aiming at the problem of bipartite leaderless consensus and bipartite tracking consensus,distributed output feedback control laws are designed respectively.Then the stability is analyzed by Riccati equation,Hurwitz matrix and Jordan decomposition technology,so that the multi-agent system can achieve the bipartite consensus under certain conditions.In the end,numerical simulations are used to show the validity of the theoretical results in this article.Furthermore,this paper considers that the relative output information of neighboring agents can be obtained directly in some practical applications.Therefore,the bipartite leaderless consensus and bipartite tracking consensus problems on the signed digraph are studied again based on the reduced-order observer,and the distributed control laws based on output feedback are constructed respectively.This protocol does not need to obtain the absolute output information of neighboring agents,but depends on the relative state of the observer and the relative output of the neighboring agent.Similar to the previous part,we use the same method to analyze the stability of the system.At last,numerical simulations are given to show the effectiveness of the reduced-order observer in this article.