I brewed a BigW 19L pot extract batch yesterday using this 2000W induction stove:
http://www.kmart.com.au/product/2000w-induction-cooker/627857?COLLCC=2333981366&
I had the pot full to within an inch of the top with 1.050 wort.
It took about 40 minutes to get to the boil (from ambient temp), I will insulate next time to speed this up (I was outside so there was a slight breeze). I had the lid on to bring it up to the boil but was watching like a hawk to avoid a boilover which I narrowly avoided.
Once It came to the boil, a setting of '6' out of 9 held a good rolling boil with no lid or insulation - I had assumed that any setting other than '9' would have just lazily cycled between full on and full off, but it appeared to actually have some sort of regulation, so the heat setting was actually useful - otherwise I would have boiled over a lot, as on 9 the boil was quite furious.
All up, I boiled for about 70 minutes, didn't skip a beat.
No burnt wort on the bottom of the pot, but there was a ring of 'congealed' wort / break on the bottom of the pot once I emptied it as mentioned by Tex above - this didn't concern me but might worry others.
For the price ($50) - I will be using this again and again with no real desire to buy a decent gas burner for outdoor brewing (until this unit dies, then I will reevaluate...)