Some applications of rational matrices to problems in systems theory

TLDR: In this article, the residue theorems of rational A-matrices having complex variables (A) and the associated rational matrix functions with square matrix variables were derived by employing the generalized Cauchy' s integral theorem.

Abstract: This paper deals with the residue theorems of rational A-matrices having complex variables ( A) and the associated rational matrix functions with square matrix variables. First, some fundamental properties of A-matrices and the associated matrix poly. normals with square matrix variables are defined by employing the Cauchy' s integral theorem. Then, a new matrix residue theorem is derived via the generalized Cauchy' s integral theorem. Finally, the block partial fraction expansion and spectral factorization of rational A-matrieos are developed via the newly extended matrix residue theorem.