Finite-Time Bipartite Consensus for Second-Order Multi-Agent Systems with Cooperation and Antagonism

This paper considers the finite-time consensus problem of second-order multi-agent systems(MASs) under cooperative and antagonistic interactions. Firstly, the distributed control protocol is formulated for the finite-time consensus of the second-order MASs with cooperative networks. On this basis, the signed graph is introduced to describe the different interactions between the agents, which takes positive and negative values for cooperation and antagonism, respectively. Finite-time bipartite consensus problem is realized for second-order MASs under undirected signed graphs by utilizing homogeneity with dilation and graph theory. Moreover, under the undirected signed graphs, the conditions for the emergence of bipartite consensus of second-order systems are analyzed emphatically by the simulation examples, which are given to illustrate the effectiveness of the proposed theoretical results.