Pinning consensus analysis of multi-agent networks with arbitrary topology

In this paper the pinning consensus of multi-agent networks with arbitrary topology is investigated. Based on the properties of M-matrix, some criteria of pinning consensus are established for the continuous multi-agent network and the results show that the pinning consensus of the dynamical system depends on the smallest real part of the eigenvalue of the matrix which is composed of the Laplacian matrix of the multi-agent network and the pinning control gains. Meanwhile, the relevant work for the discrete-time system is studied and the corresponding criterion is also obtained. Particularly, the fundamental problem of pinning consensus, that is, what kind of node should be pinned, is investigated and the positive answers to this question are presented. Finally, the correctness of our theoretical findings is demonstrated by some numerical simulated examples. (general)