Looks like it might be the Hafele Frontino system.

Knowing that's designed by Mick DiGiulio, it could have a hefty price tag as it's designed, but I'll bet someone could hack that using: lightweight closet door hardware? pocket door hardware to roll on bottom? curtain track? You might find someone who has adapted this if you search for the designer's name.

It's custom to work with the false wall.

Look at a company called Johnson Hardware. They make all kinds of unusual track hardware. I got my pocket door hardware from them, which is not that huge, cumbersome framing process. Just the nice hardware.

Another place to look is Lee Valley once you decide what you really want. Van Dyke is also great for unusual things.
Rockler has actual appliance garage components, but they're actually appliance garages, not this monstrous thing you're attempting! :)

I really, really, really wanted to do this. But it didnt work out for me because of space issues.

I was looking at hardware from Sugatsune, I thought one of these two, or one of their sliding systems would be possibilities. I liked the lateral hinges best, at least at initial stages, because they close flush.

http://www.sugatsune.com/Architectural_Hardware_News/Rev4.LIN-X_Flyer_0614.pdf
http://www.sugatsune.com/products/ProductDetails.cfm?CATID=12&SUBCATID=1&PRODUCTID=MFS%2DW%20Series

Cool! Agree, check johnson hardware. I got the sliding barn door kit (they sell individual pieces). Amazon had the best pricing when I purchased last fall.

The biggest issues are hiding guides and tracks- particularly the bottom.
Hafele will have the most options for dealing with bottom guides or track, door thickness (5/8 to 2-1/2") and weight- It's not the frontino system
Take a look at the EKU Clipo series for doors from 5/8 to 1" thick

Thanks for all the ideas. The Johnson Hardware option seems to be the closest match, as it is suspended from above with no lower track. I do wish that the panels, when closed, would be flush with the stationary panel in the middle though. it looks like they would have to be offset with the Johnson Hardware options.

Pretty sure Johnson uses a guide on bottom, at least all the ones I've done did. Also have to hide the top track.
Hafele has a similar system for bottom but smaller pins and hidden top.
Flush closed would be fronting but the tracks will show.

Sorry, no idea, but next kitchen I do, I'm installing one!!

Go to www.cabinetparts.com, and then give them a call. Their reps are geniuses at figuring out these kinds of problems!

Here is a link that might be useful: Cabinetparts web site