The preservation of both robust stability and weighted robust performance properties of controlled linear time-invariant single input single output (SISO) systems is studied, when performing substitutions (of the complex Laplace variable s) by a particular class of rational strictly positive real functions (SPR functions), the so-called strictly positive real functions of zero relative degree (SPR0 functions). Concerning weighted robust performance and model-matching, we provide some results on preservation of controller optimality.