Seeking group consensus in networks of dynamic agents under directed topology

In this paper we investigate the s groups consensus problem by giving a kind of new protocol in directed networks with fixed topology. The sufficient conditions which group consensus can reach under the given protocol are obtained and the consensus process could be controlled because of the newly added feedback controllers in our protocol. Then the dynamic performance of our protocol is discussed and several criteria are presented to infer the consensus space of different groups based on graph theory and matrix theory. Numerical examples are addressed to demonstrate the effectiveness of the proposed theoretical results.