On the use of right-coprime factorizations in distributed feedback systems containing unstable subsystems

In this paper, we prove that every rational transfer function matrix has a right-coprime factorization in
{\cal Q}^{n \times n}
, and that a right-coprime factorization contains all the information about the domain and range of an unstable operator. We also derive a general necessary and sufficient condition for feedback stability that is applicable even to nonlinear systems, and show that right-coprime factorizations arise naturally when this general condition is applied to linear time-invariant systems.