Realisable in this sense means that the impedance can be constructed from a finite (hence rational) number of discrete ideal passive linear elements (resistors, inductors and capacitors in electrical terminology).
A couple of generalizations are sometimes made, with intention of characterizing the immittance functions of a wider class of passive linear electrical networks.
The impedance Z(s) of a network consisting of an infinite number of components (such as a semi-infinite ladder), need not be a rational function of s, and in particular may have branch points in the left half s-plane.
Thus, a possibly irrational function Z(s) is PR if and only if Some authors start from this more general definition, and then particularize it to the rational case.
So by extending the definition of PR to matrix-valued functions, linear multi-port networks which are passive may be distinguished from those that are not.