Under the connected bipartite graph topology, the group-consensus protocol design problem is investigated for
a class of first-order multi-agent systems with and without time delay respectively, and several new results are presented. Firstly, based on the properties of the bipartite graph, a control protocol is designed and the group-consensus problem is studied for the systems without time delay, and the final convergence states are given with respect to the initial conditions. Then, the group-consensus problem of the systems with time delay is investigated, and the maximum allowed delay is obtained. Finally, the simulation result shows the correctness of the proposed method.