On the Kronecker Canonical Form of Singular Mixed Matrix Pencils

Dynamical systems, such as electric circuits, mechanical systems, and chemical plants, can be modeled by mixed matrix pencils, i.e., matrix pencils having two kinds of nonzero coefficients: fixed constants that account for conservation laws and independent parameters that represent physical characteristics. Based on dimension analysis of dynamical systems, Murota (1985) introduced a physically meaningful subclass of mixed polynomial matrices. For this class of mixed matrix pencils, we provide a combinatorial characterization of the sums of the minimal row/column indices of the Kronecker canonical form. The characterization leads to an efficient algorithm for computing them. This is an extension of the result by Iwata and Shimizu (2007) on matrix pencils whose nonzero entries are all independent parameters.