Consensus of Multiweighted Second-Order Networks With Directed Topologies

We consider consensus of multiweighted second-order networks with directed topologies. Multiweight means that the position state and velocity state have multiple inner coupling matrices (ICMs) and outer coupling matrices (OCMs) respectively. As far as we know, no research on second-order networks has studied multiweighted networks. To solve the problem of multiweighted networks, we utilize rearranging variables’ order technique (ROT). The key of ROT is taking the elements of ICMs as the coefficients of OCMs. Therefore, the information of ICMs can be made full use to reach consensus. Different from other studies on second-order networks, we consider both cooperative and competitive relationships between nodes and inside nodes. The corresponding numerical simulation verifies our theory.