Dell UltraSharp 27 User Manual page 44

Go to System Settings.
In the drop-down menu of When I press the power button, there are a few options
for selection namely Do nothing/Sleep/Hibernate/Shut down, and you can select
Sleep/Hibernate/Shut down.
NOTE: Do not select Do nothing, otherwise monitor power button cannot sync
with PC system power state.
44 | Setting Up the Monitor