Computing balanced realizations of transfer function matrics using householder transformations

A method involving Householder transformations is presented for obtaining a minimal Jordan form realization of a transfer function matrix from its partial fraction expansion. The Jordan form simplifies the determination or the Gramians while the minimality of the realizations assures the numerical stability of the Chclesky decomposition of both Gramians. Finally the matrix requiring SVD to complete the transformation to balanced form is simplified to an upper triangular matrix by performing the aforementioned Cholesky decomposition in a complementary manner.