Semi-cancellable fractions in system theory

In this paper, we propose to define the transfer function of a system in a new way, namely as a semi-cancellable fraction (SCF), i.e. a fraction in which unstable pole-zero cancellations are not allowed. Within this new framework, it is possible to be rigorous and coherent in dealing with the stabilizability of a system from an input-output viewpoint, not focusing on the stabilizability of infinite dimensional input-output systems.<
>