Saturn Controller Options for PS4

Does anyone know if any of the following controllers work on PS4:

Sega Saturn USB PC/Mac Pad
Sega Saturn PS2 Edition Pad via Converter?
Regular Sega Saturn pad to PS4 converter?

Wondering what my options are. It's rare to see this discussed anywhere. The PC Saturn pad worked on PS3 without a converter and IIRC the PS2 version worked on 360 with a converter.

Also bonus question: if a converter is needed, or even if it's not, does anyone have any experience with input lag, does it lag at all?

Thanks.