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This paper deals with the leader-following consensus of discrete-time multi-agent systems subject to both position and rate saturation. Each agent is described by a discrete-time general linear dynamic with actuator subject to position and rate saturation. A modified algebraic Riccati equation and low-gain feedback design technique are used to construct both state feedback and output feedback control protocols. It is established that a semi-global leader-following consensus can be achieved when the system is asymptotically null controllable with bounded controls and a leader agent has a directed path to every follower agent. Finally, several simulations are carried out to illustrate the results. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]