Parametric model for 2D real scattering Schur polynomials

In the field of multidimensional stability theory so called scattering Hurwitz polynomials (in the continuous case) and scattering Schur polynomials (in the discrete) case play a crucial role. In the present paper a parametric representation for real two-variable scattering Schur polynomials is given. The following features of this model makes it best suited for the computer based design of 2-D systems, namely no dependencies between the real valued parameters, coverage of the whole class of 2-D scattering Schur polynomials, and the coefficients of the polynomials are rational functions of the parameters. The synthesis of two-dimensional (2-D) lossless networks and Householder matrices form the basis of our considerations