Just for a little context the video relates to modelling a flyback driven constant current LED driver and Io(s) is the output current and d(s) is the PWM signal. So Gd(s) is the transfer of the desired output over the controlled input. First appearances, the man, Marcos Alonso, seems brilliant, a true engineer reducing by reasonable assumptions complex problems to manageable solutions. But to confirm or understand his analysis would take many hours of derivation as quite reasonably for the video he only provides the results with basic steps. But thanks for the question, I learned a little, un piquito.