In this chapter, the analysis problem of peak-to-peak gain is studied for 2-D positive systems with interval time-varying delays. Directional delays in the state vectors are heterogeneous and time-varying, which are confined within different ranges with lower bounds other than zero. Novel comparison techniques involving interval state estimations subject to peak values of exogenous disturbances are presented and a characterization of \(l_\infty \) -induced norm of the input-output operator is formulated. The obtained \(l_\infty \) -gain characterization is then utilized to establish necessary and sufficient conditions in terms of linear programming (LP) settings for \(l_\infty \) -induced performance with a prescribed attenuation level. Applications to \(l_\infty \) -gain control problem via static output-feedback controllers are also discussed. Numerical examples and simulations are given to illustrate the effectiveness of the proposed method.