The semi-global output consensus problem for multiagent systems depicted by discrete-time dynamics subject to external disturbances and input saturation over switching networks is investigated in this paper. Assume that only a small part of subsystems have directly received the output of the exosystem. The distributed consensus algorithms are proposed by adopting the low-gain state feedback and the modified algebraic Riccati equation. Then, the outputs of all subsystems can reach synchronization asymptotically with those of the exosystem by using the proposed consensus protocols on some preconditions. Both the connected switching networks and the jointly connected switching networks are considered for the semi-global output consensus problem, respectively. Some numerical simulation results are shown to validate the theoretical analysis.