ABSTRACT
The proper rational functions H(z) arising in discrete-time systems can be treated in a similar manner. One can write
H(z) = B(z) A(z)
,
where A and B are coprime, Schur-stable (hence proper) rational functions. Coprimeness means having no unstable zeros (i.e., in the closed disc |z| ≥1) in common. For example, if
H(z) = 1 z − 1 ,
then one can take
A(z) = z − 1 z −λ , B(z) =
z −λ for any real number λ such that |λ| < 1. The set of Schur-stable rational functions is denoted by RS(z).
