Jordan form realization via singular value decomposition

A method is presented for computing a minimal J-form realization ( A, B, C) of a transfer function matrix from its partial fraction expansion (PFE). The decoupling inherent in the Jordan form enables the computational algorithm for the general multipole case to be developed by considering the case of a transfer function matrix having one pole of multiplicity α. After developing matrix equations relating the column of C and rows of B to the fraction expansion coefficient, a single sweep method which utilizes orthogonal matrices generated sequentially by singular value decomposition (SVD) is developed for determining the column of C, rows of B and the structure of the J-form for A. At the ith state in the sequence, the matrix requiring SVD is composed from PFE coefficient matrices and matrices generated by previous SVDs. Other computational aspects of the proposed method are presented and discussed