Powershift transmission was highly publicized in 2009 / 2010 IIRC for the "Large" Ford Range (SMax, Mondeo, Galaxy).
During that time I was working at the Volvo dealership - that was together with Ford, and we received a memo, that Powershift would have been available on 2.0 litre diesel (4 cylinder, 136 ps, PSA engine - in common with Citroen, Peugeot, and BTW, Ford). Short after the memo, we received a V50 with that dual clutch gearbox, that promised very quick gear changes - Volvo's Geartronic wasn't a real quick automatic gearbox, and many customers complained about that - and indeed it had. But it was strange. Not comfortable, not Volvo-ish if you know what I mean. I had that car as company car for about two weeks, before selling it. Odd enough, the car stalled with the engine turning off if you tried to get off quick, or during sharp turns (i.e. when coming out of a parallel parking). Like when releasing the clutch too quick. A leap and no engine. I looked like a rookie driver
We runned a gearbox software update before selling the car. It was mandatory by VCC. I sold the car personally, and the customer came back several times for gearbox problems. VCC always paid for those problems - even if the warranty was expired.
Powershift gearbox on Volvo cars was short lived. With the last C30 / S40 / V50 facelift (when LED DRL in the fog lights were introduced, 2011 IIRC) the whole Powershift and 2.0 4-pot PSA engine were dropped, in favour of 2 litres 5 cylinders with 163 and 177 ps (D3 and D4 versions) equipped with the good ol' Geatronic gearbox.
Double clutch gearboxes and automatically operated manual gearboxes are mostly shite.
Ford's Powershift has the problems we all know
Alfa Romeo Selespeed (single clutch) was a complete disaster
Ferrari's early F1's (355 and 360 models) were a complete disaster... but really, garbage
VW's DSG has an expiration date... that's 150k km or 3 years on diesel engined cars, less on GTI versions
Citroen's CMP ... what the Hell