Can we first define what is the Pink Floyd sound - its caracteristics respect to the harmony, melody, instruments - and then continue the thread? I can imagine what every response means, where do you find a peace of Pink Floyd in the named bands, but then it results Pink Floyd influenced the whole modern music until today, which is undoubted but this way the thread becomes a little bit confusing.
I don't think you can define the 'Pink Floyd sound' in any sort of satisfactory way. They were a complex group that covered a lot of ground over a career that's not done yet, apparently. People hear music differently, and associate different things with different weights based on their own personal experience with a band. For some it's the ringing solos of Gilmour, for others it's the personal feeling of Waters, or the psychedelic qualities, or the experimentation with song structure, or a dreamlike feel, the list goes on...
The reality is that influence is a nebulous thing, and all of the bands listed can easily be argued to have been shaped in one way or another by Floyd. You may feel that the differences are too stark, but the OP asked for influence, not copying. Floyd is a tough band to copy satisfactorily, as they were masters of minimalism (Gilmour, Mason), soundscapes (Wright) and emotional tension (Waters).
And not all bands could be listed here. Nobody is putting Slayer or Danko Jones or Maroon 5 forward. Just bands that consciously work outside traditional song formats and experiment a little. Or ones that go for a more ethereal feel, though I think those bands share less with Floyd, myself, but that's, like, only my opinion, man.
My vote has already been listed, but Ancestors is a rare band that has been heavily influenced but doesn't sound like a tribute act. They use way more distortion than Floyd ever did, but they capture that same sense of ebb and flow, tension and release that made Floyd so powerful. To me, anyway...