Optimal 2-D separable-denominator approximants for 2-D transfer functions

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 <(gamma)over cap> parameters 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 <(gamma)over cap> parameters 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.