On computing normalized coprime factorizations of periodic systems

Abstract

A numerically reliable state space algorithm is proposed for computing normalized coprime factorizations of periodic descriptor systems. A preprocessing step is used in the algorithm to convert the initial problem for possibly non-causal systems into a simpler problem for causal periodic systems. The main computational ingredient here is the computation of a coprime factorization with causal factors which is addressed by computing right annihilators of an appropriately extended system via periodic pencil manipulation algorithms. The solution of the normalized coprime factorization problem for a causal system involves the solution of a generalized periodic Riccati equation. The proposed two steps approach is completely general, being applicable to periodic systems with time-varying dimensions.