Group consensus tracking control of second-order multi-agent systems with directed fixed topology

This paper focuses on studying the group consensus tracking issue of continuous-time second-order multi-agent systems (MASs) under directed fixed topology. A new protocol is introduced under the assumption that all the subgroups satisfy the in-degree balanced condition. For MASs with two subgroups, we first establish the relationship between the positive stability of matrix H and the connectedness of the topology graph. Then, we prove that MASs can achieve group consensus tracking if the system parameters satisfy some inequalities and matrix H is positive stable. Moreover, our paper extends the results for MASs with two subgroups to multiple χ-group consensus tracking. Especially, for a special graph with acyclic partition, a necessary and sufficient condition of χ-group consensus tracking is established. Finally, simulation examples are given to illustrate the effectiveness of our results.