On the factorization of rational matrices

Many problems in electrical engineering, such as the synthesis of linear n ports and the detection and filtration of multivariable systems corrupted by stationary additive noise, depend for their successful solution upon the factorization of a matrix-valued function of a complex variable
p
. This paper presents several algorithms for affecting such decompositions for the class of rational matrices
G(p)
, i.e., matrices whose entries are ratios of polynomials in
p
. The methods employed are elementary in nature and center around the Smith canonic form of a polynomial matrix. Several nontrivial examples are worked out in detail to illustrate the theory.