Sharing the same controller without constantly USB syncing?

Sharing the same controller without constantly USB syncing? - Crop unrecognizable female on modern monitor with video game on screen near ethnic partner

I have a PS Vita TV and a PS3 but only one DualShock controller. Whenever I switch between systems I have to briefly plug the controller into the USB port of the system I wish to start using. This is becoming a bit annoying as I want to have the Vita TV tucked away.

Is there anyway to use the controller on a different system without having to re-pair it via USB?






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The USB port does change the input lag?!




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Images: cottonbro, Karolina Grabowska, Karolina Grabowska, Brett Sayles