Approximation when deriving buck closed loop transfer function
I think they assume that the average of the square wave generated by turning on and off the PMOS transistor is \$&lt;V_x&gt;=\text{D}V_{in}\$ and it doesn't look like they include the \$R_{on}\$ voltage drop associated with the PMOS transistor when it is on.

Now, \$V_{\text{o}}\$ isn't exactly equal to \$V_x\$ because of the voltage drop due to the series resistance associated with output inductor, but they should be really close.

So, I think of it as \$V_x\$ being a square wave without filtering with its average being portion of the input voltage (\$\text{D}V_{in}\$). And \$V_o\$ is the output voltage after filtering which should be the same as the average of the \$V_x\$ waveform minus the voltage drop caused by the output filter.