Hey everyone. I know this is a super old issue but Microsoft has never fixed or addressed it. There are a couple things that help with this but none of them are solutions, more workarounds. The first, already mentioned is to plug in your controller.
The second is to get the official wireless adapter from Microsoft so you aren't using Bluetooth and another slightly less known workaround is to turn off the vibration function in your game settings.
The last one, Turning off vibrations, isn't nearly as effective as the first two but it's something for those that don't have a long cord or a wireless dongle. Turning off the vibration will only increase fps slightly (+20 fps for me) and it wont effect the input lag or stuttering.
Disabling/bypassing Bluetooth headsets and controllers are the only complete work-arounds right now.
This issue is completely controller specific and so using a Dual-shock 4 via Bluetooth has none of the issues although setting it up comes with it's own headaches. lol
I had this problem recently when playing several PC games with my xbox controller using bluetooth. The solution is to update your controller firmware. This can be done by downloading the xbox accessories app in the microsoft app store, connecting your controller to the pc wired, and using the app to update the firmware. Cheers!
