This work is concerned with the leader-following control design for linear multi-agent systems with norm bounded uncertainties as well as constrained inputs. The purpose is to design a distributed control algorithm for the followers to track their leader's states without having access to the latter's inputs, in addition to respecting the predefined bounds of the input saturation constraints. For the control design, the H∞criterion is used to minimize the tracking error of the agents. Knowing the initial state of the followers, sufficient LMI-based conditions are proposed to solve the leader tracking problem and restrict the amplitudes of the followers inputs in predefined areas. The efficiency of this method is illustrated through the simulation of a group of two mass-spring systems.