The main purpose of this article is to investigate the consensus of linear multiagent networks with time-varying characteristics under sampled-data communications, where the time-varying characteristics include both time-varying topologies and the node's linear time-varying dynamics. By using the decoupling method, we prove that the sampled-data consensus problem of multiagent networks is equal to the stability problem of sampled-data systems. Then, the globally asymptotical consensus is investigated for multiagent networks with time-varying characteristics by virtue of the Lyapunov function method. It should be noted that when the Lyapunov function method is utilized to investigate the stability problem of control systems, it is always assumed that the derivative of the constructed Lyapunov function is not more than zero. This assumption is removed here and as a replacement, the average value of the derivative of the Lyapunov function in a period to be negative is needed.