| In multi-agent systems, cooperation and antagonism are two common interactions among agents. For this kind of multi-agent systems, this paper considers the bipartite consensus problem over a signed digraph in the presence of time-delays. Taking double-integrator multi-agent systems as the starting point, for with and without time-delays, we design distributed protocols, respectively. It is shown that in the absence of time-delays,if the communication topology among agents is structurally balanced and has a spanning tree, then the multi-agent systems achieve a bipartite consensus by appropriately selecting gains. In particular, the states of agents will converge to zero regardless of initial positions and velocities if the communication topology is structurally unbalanced. By using the tools of algebraic graph theory and frequency domain theory sufficient conditions for ensuring a bipartite consensus are given in the presence of time-delays. Furthermore, it is proved that the upper bound on the admissible communication time-delay is closed related to the communication topology among agents. |
