I am trying to understand the properties of positive real (PR) and strictly positive real (SPR) transfer functions. If given a transfer function I know how to determine whether or not the function is PR/SPR, however I'm not sure how to approach the following example.
Say we are given two positive real transfer functions: $G_{1}(s)$ and $G_{2}(s)$
How can I tell if the sum $$ G_{1}(s) + G_{2}(s)$$ or the product $$ G_{1}(s) * G_{2}(s)$$
is PR/SPR?
Intuitively, I think the sum is SPR, but as for the product I am uncertain. Either way, is there a framework I can use to approach this or does anyone know of a proof I could look at?