This paper is concerned with the optimal approximation of a general 2-D transfer function by a separable-denominator one with stability preservation. To preserve the stability, the two one-variable denominator polynomials of the reduced model are both represented in their bilinear Routh continued-fraction expansions. The bilinear Routh .Yparameters of the two one-variable denominator polynomials and the coefficients of the two-variable numerator polynomial are then determined such that a frequency-domain L 2 -norm is minimized. The main advantage of searching bilinear Routh .Yparameters instead of denominator coefficients is that the stability constraints on the new decision parameters are simple bounds. To facilitate using a gradient-based algorithm, an effective numerical algorithm is also provided for computing the performance index and its gradients with respect to the decision variables. 213

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