Necessary condition of consensus for affine multi-agent systems under time-varying directed networks

This work studies the necessary condition for a class of affine multi-agents system under time-varying directed network. By means of notion ∞-adjoin graph of time-varying network we do the decomposition of ∞-adjoin graph for the time-varying directed network, the system consists of several independent basic components and non-independent basic components of the system. Under some mild conditions on system dynamic behavior and network topology, it is shown that system achieve consensus only if the network has only one independent basic component for the network. This results is very similar to that of linear multi-agent systems under time-invariant directed networks.