PS4 controllers can be a headache to recognize. This tutorial should help.
The following procedure has been tested with a PS2 version 2 controller. It may be different for a version 1.
Here's how to get your PS4 controller recognized:
PS
and SHARE
buttons simultaneously for 5 seconds.Now your controller should be paired and working without even needing to be reconfigured.
Procedure source: https://forum.recalbox.com/topic/8920/a-lire-manettes-ps4
Image sources: here and here
The controller can, of course, be switched off. To do so, press and hold the PS button for 10 seconds.