Positive-real functions, often abbreviated to PR function or PRF, are a kind of mathematical function that first arose in electrical network synthesis. They are complex functions, Z(s), of a complex variable, s. A rational function is defined to have the PR property if it has a positive real part and is analytic in the right half of the complex plane and takes on real values on the real axis. In symbols the definition is, In electrical network analysis, Z(s) represents an impedance expression and s is the complex frequency variable, often expressed as its real and imaginary parts;