Bipartite consensus of double-integrator multi-agent systems with nonuniform communication time delays

In this paper, the bipartite consensus problem is addressed for a class of double-integrator multi-agent systems with antagonistic interactions. The cases with and without communication time delays are considered. In particular, if the communication time delays are not taken into account, the bipartite consensus of the studied multi-agent systems with directed signed graph can be achieved by the proposed distributed controller. If the nonuniform communication time delays are considered, the bipartite consensus of the considered multi-agent systems with undirected signed graph can be achieved if the time delays are less than a derived upper bound. Moreover, we propose an algorithm to solve the so-called grouping problem. Finally, some numerical examples are provided to illustrate the correctness of the results.

Automated summary

This paper addresses the bipartite consensus problem for double-integrator multi-agent systems with antagonistic interactions, considering cases with and without communication time delays. It is shown that bipartite consensus can be achieved with a distributed controller if communication time delays are not considered, and if nonuniform delays are less than a certain upper bound for systems with undirected signed graphs. Additionally, an algorithm for solving the grouping problem is proposed.