Numerical computation of a coprime factorization of a transfer function matrix
The problem of computing a (right) coprime factorization \(N_ r(\lambda)D_ r^{-1}(\lambda)\) of a given rational transfer function matrix \(H(\lambda)=D_ L^{-1}(\lambda)N_ L(\lambda)\) has a well- known algebraic but not an efficient numerical solution. The authors reformulate this problem as a problem of constructing a minimal polynomial basis of the right nullspace of a matrix pencil \(\lambda\) B-A associated to the polynomial matrix \(P(\lambda)=[N_ L(\lambda),D_ L(\lambda)]\). This latter problem is solved by transformating \(\lambda\) B-A to a generalized Schur form of a pencil by numerically backward stable algorithms as analyzed in the first author's Ph.D. thesis. The complete algorithm is presented and illustrated by two numerical examples of coprime factorizations chosen from the literature.
scientific article; zbMATH DE number 4025262
scientific article