Computation of Normalized Coprime Factorizations of Rational Matrices

Abstract

We propose a new computational approach based on descriptor state space algorithms for computing normalized coprime factorizations of arbitrary rational matrices. The proposed approach applies to both continuous- and discrete-time rational transfer-function matrices and shows that each rational matrix possesses a normalized coprime factorization with proper factors. The new method is conceptually very simple, essentially reducing the original factorization problem to one for proper systems. The main computation consists in solving an appropriate generalized algebraic Riccati equation.