Representing feedback circuitry as two-port networks
Even though it is hard to believe the two-port parameters are used to make life easier and give a simple representation of the feedback system.

Focusing on the simple representation, the strategy is as follows. First the common quantities on the input side and the output side have to be determined. Then suitable two-port parameters that have these as independent variables have to be found. For this step a table with all major two-port parameters could prove useful.

Looking at the series-shunt example (the right one in the bottom row) the networks share a common current at the input (I1) and have a common voltage at the output (V2). This results in h-parameters since they have I1 and V2 as independent variables.

For the shunt-series connection (left one in the first row) we find V1 and I2 as common quantities and consequently the g-parameters are used.

Ok, since I'm halfway through: 


series-series (first row, right), I1 and I2 are in common, z-parameters
shunt-shunt (second row, left), V1 and V2 are in common, y-parameters