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This paper studies global leader-following consensus of a group of networked multi-integrator systems subject to control input saturation. A weighted nonlinear state feedback control law is proposed to solve this problem. Both the case of a fixed undirected communication topology and the case of a switching undirected communication topology are considered. We show that leader-following consensus can be achieved by using the proposed control laws when the communication topology is connected or jointly connected. Simulation results are given to illustrate the theoretical results.