# Rational and polynomial matrix factorizations via recursive pole-zero cancellation

- Authors
- Journal
- Linear Algebra and its Applications 0024-3795
- Publisher
- Elsevier
- Publication Date
- Identifiers
- DOI: 10.1016/0024-3795(90)90144-2
- Disciplines

## Abstract

Abstract We develop a recursive algorithm for obtaining factorizations of the type R(λ)=R 1(λ)R 2(λ) where all three matrices are rational and R 1(λ) is nonsingular. Moreover the factors R 1(λ) and R 2(λ) are such that either the poles of [ R 1(λ)] -1 and R 2(λ) are in a prescribed region Γ of the complex plane, or their zeros. Such factorizations cover the specific cases of coprime factorization, inner-outer factorization, GCD extraction, and many more. The algorithm works on the state-space (or generalized state-space) realization of R(λ) and derives in a recursive fashion the corresponding realizations of the factors.

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