This paper studies the H_∞ consensus problem for linear heterogeneous discrete-time multiagent systems (MASs). For a special kind of nonlinear matrix inequality, a novel method is provided to make these inequalities turn into some equivalent conditions that can be solved by utilizing the LMI toolbox. According to this method, a necessary and sufficient condition of H_∞ consensus for linear heterogeneous discrete-time MAS with output feedback control scheme and a corresponding iterative algorithm are proposed, respectively. Moreover, by employing these results, a necessary and sufficient condition that makes a general linear system with one kind of constrained controller achieve H_∞ control is provided. Finally, two numerical examples are given to illustrate the validity of our schemes.