  This paper studies coordination problem for time-varying networks suffering
from antagonistic information, quantified by scaling parameters. By such a
manner, interacting property of the participating individuals and antagonistic
information can be quantified in a fully decoupled perspective, thus benefiting
from merely directed spanning tree hypothesis is needed, in the sense of usual
algebraic graph theory. We start with rigorous argument on the existence of
weighted gain, and then derive relation among weighted gain, scaling parameter
and Laplacian matrix guaranteeing antagonistic information cannot diverge
system state. Based on these arguments, we devise coordination algorithm
constrained by topology-dependent average time condition, thus relaxing the
examination of directed spanning tree requirement for the union graph that is
usually intractable. Moreover, the induced theoretical results are applied to
time-varying networks with several mutually uninfluenced agents, in
accompanying with some discussions and comparisons with respect to the existing
developments.
