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The minimization problem of frequency-weighted l2-sensitivity subject to l2-scaling constraints is formulated for two-dimensional (2-D) state-space digital filters described by the Roesser model. It is shown that the Fornasini-Marchesini second model can be readily imbedded in the Roesser model. An iterative method is developed to solve the constrained optimization problem. This method converts the problem into an unconstrained optimization formulation by using linear-algebraic techniques and solves it by applying an efficient quasi-Newton algorithm. A case study is presented to illustrate the utility of the proposed technique.