Synthesis of multidimensional lossless transfer functions via sum of squares of polynomials

In this paper, a novel technique for synthesis of lossless transfer function for multidimensional systems is given. It utilizes semidefinite programming used to find a sum of squares representation. Such possibility follows from the Hilbert´ s theorem which refers to a representation of real forms as a sum of squares. The usefulness of the algorithm is illustrated by one-, two-, and three-dimensional examples.