Rational and polynomial matrix factorizations via recursive pole-zero cancellation

AbstractWe develop a recursive algorithm for obtaining factorizations of the type R(λ)=R1(λ)R2(λ) where all three matrices are rational and R1(λ) is nonsingular. Moreover the factors R1(λ) and R2(λ) are such that either the poles of [R1(λ)]-1 and R2(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