Group consensus in multi-agent systems with switching topologies and time delays*

In this paper, we investigate the group consensus problem for discrete-time multiagent systems with switching topologies and bounded time delays. The analysis in this paper is based on nonnegative matrix theory and graph theory. Under the assumption of common inter-group influence, the group consensus problem is proved to be solvable, if the union of the communication topology across any time interval with some given length contains group spanning trees. It is also shown that the nonzero in-degree groups finally converge to convex combination of the consensus states of the zero in-degree groups. The effectiveness of the theoretical results is finally demonstrated by the simulation example.