In this work, robustness and convergence properties of model reduction are investigated for discrete two-dimensional (2D) systems in the Fornasini-Marchesini (F-M) model with polytopic uncertainties. The goal is to design a reduced order model minimizing H-infinity performance in a known finite-frequency (FF) area of the noises able to reproduce the behavior of the uncertain 2D original system. Using Lyapunov function and generalized Kalman Yakubovich Popov (gKYP) lemma, sufficient conditions for the existence of the FF reduced order design approach are formulated as feasibility of a set of Linear Matrix Inequalities (LMIs). Numerical simulations are given to illustrate the validity and feasibility of the designed reduced-order model.