Structural Identification: The Computation of the Generic McMillan Degree

The McMillan degree of a transfer function model is one of the most important structural characteristics of a system. In this paper the problem of identifying the generic McMillan degree of a rational matrix is considered. The transfer function matrices of interest are those referred to as Structured Transfer Function (STF) matrices and have certain elements fixed to zero, some elements being constant and other elements expressing some identified dominant dynamics of the system. For the family of STF matrices the problem of determining the generic McMillan degree is considered using genericity arguments and an optimisation procedure based on path properties of nonnegative integer matrices. A novel approach is introduced that exploits the structure of integer matrices and this leads to an efficient new algorithm for computation of the generic value of the McMillan degree. Links are made to standard problems of optimisation and in particular to the optimal assignment problem. The problem examined here belongs to the general area of Structural Identification where the evaluation of structural characteristics of STF models is under investigation with robust computational methods. Such problems are of interest to large scale system studies.