In control theory, a closed-loop transfer function is a mathematical function describing the net result of the effects of a feedback control loop on the input signal to the plant under control.

The closed-loop transfer function is measured at the output. The output signal can be calculated from the closed-loop transfer function and the input signal. Signals may be waveforms, images, or other types of data streams.

An example of a closed-loop block diagram, from which a transfer function may be computed, 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:

${\displaystyle G(s)}$ is called the feed forward transfer function, ${\displaystyle H(s)}$ is called the feedback transfer function, and their product ${\displaystyle G(s)H(s)}$ is called the open-loop transfer function.

We define an intermediate signal Z (also known as error signal) shown as follows:

Using this figure we write:

Now, plug the second equation into the first to eliminate Z(s):