An algorithm for direct identification of passive transfer matrices with positive real fractions via convex programming

The paper presents a new algorithm for the identification of a positive real rational transfer matrix of a multi-input–multi-output system from frequency domain data samples. It is based on the combination of least-squares pole identification by the Vector Fitting algorithm and residue identification based on frequency-independent passivity constraints by convex programming. Such an approach enables the identification of a priori guaranteed passive lumped models, so avoids the passivity check and subsequent (perturbative) passivity enforcement as required by most of the other available algorithms. As a case study, the algorithm is successfully applied to the macro-modeling of a twisted cable pair, and the results compared with a passive identification performed with an algorithm based on quadratic programming (QPpassive), highlighting the advantages of the proposed formulation.