This paper studies the leader-following consensus problem for a group of agents with identical linear systems subject to control input saturation. We focus on two classes of linear systems, neutrally stable systems and double integrator systems. For neurally stable systems, we establish that global consensus can be achieved by linear local feedback laws over an undirected fixed or a switching communication topology. For double integrator systems, we establish that global consensus can be achieved by linear local feedback laws over a fixed communication topology and, with the help of a simple saturation function in the local feedback laws, global consensus can also be achieved over a switching undirected topology. Simulation results illustrate the theoretical results.
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