On pinning group consensus for dynamical multi-agent networks with general connected topology

In this paper, we focus on investigating group consensus of dynamical multi-agent networks via pinning scheme. The topology of the network is a general digraph, which needs neither being symmetric nor containing a spanning directed tree, and some criteria are proposed to guarantee the realization of group consensus instead of relying on other conservative assumptions presented by majority of the relevant research works, such as in-degree balance. In addition, it is interesting to find that the nodes with zero in-degree should be pinned first based on the property of M-matrix. Furthermore, an adaptive pinning control approach is developed to obtain the appropriate control gains. Finally, the effectiveness and correctness of our theoretical findings are verified by some numerical simulations.