Sensitivity Function

The ratio of the fractional change in $T\left(s\right)$ (closed-loop TF) to the fractional change in $G_p\left(s\right)$ (the plane TF)

Sensitivity function for the TF above is… $\frac{1}{1+G_P{G}_C}$

The complementary transfer function i defined as $C\left(s\right)=1-S\left(s\right)=\frac{G_C\left(s\right)G_P\left(s\right)}{1+G_C\left(s\right)G_P\left(s\right)}$