A closed-loop transfer function in control theory is a mathematical expression (algorithm) describing the net result of the effects of a closed (feedback) loop on the input signal to the circuits enclosed by the loop.
An example of a closed-loop transfer function is shown below:
The summing node and the G(s) and H(s) blocks can all be combined into one block, which would have the following transfer function:
We define an intermediate signal Z shown as follows:
Using this figure we write: