State-Space Minimal Realizations and Latent Structures of Column-Reduced and Nonsingular Polynomial Matrices

The concept of a column-reduced polynomial matrix is an important one in the theory of linear systems. The theory of Jordan chains and minimal realizations is developed for such matrices. Also, the relationships between generalized latent vectors of the nonsingular polynomial matrix and their associated generalized eigenvectors of the system map are explored in this paper. This permits the spectral analysis of an arbitrary nonsingular polynomial matrix, extending previous work for the monic case.