Weighted Consensus Problem for Multi-agent Systems

In this paper, the concept of consensus is generalized to weighted consensus, by which the bipartite consensus and cluster consensus problems can be unified in the proposed weighted consensus frame. The dynamics of agents are modeled by the general continuous-time linear systems. The interaction topology is modeled by edge- and node-weighted directed graphs. Under both state feedback and output feedback control strategies, the weighted consensus problems are transformed into the equivalent conventional consensus problems. Then, a distributed state feedback protocol and an output feedback protocol are proposed to solve the weighted consensus problems respectively. Finally, a simple example is given to illustrate the effectiveness of our proposed approaches.