This chapter addresses the problem of \(l_1\) -gain control for two-dimensional (2-D) positive systems in Roesser model and Fornasini–Marchesini local state-space (FMLSS) model with directional delays. Exact value characterizations of \(l_1\) -induced norm of the input-output operators are obtained using 2-D Z-transform approach. The obtained \(l_1\) -gain characterizations are then utilized to establish necessary and sufficient conditions in terms of linear programming (LP) settings for \(l_1\) -induced performance with a prescribed attenuation level. Finally, by utilizing a linear convex optimization approach, necessary and sufficient conditions for the existence of a state-feedback controller (SFC) that makes the closed-loop system positive, stable and has prescribed \(l_1\) -induced performance are formulated. Numerical examples and simulations are given to illustrate the effectiveness of the proposed method.