The core of the QCW DRSSTC, and the part that sets it apart from classic DRSSTC's, is that your usual fixed bus voltage (doubler/variac/boost converter/whatever) is replaced by a regulated step-down converter. The converter modulates the pulsed output from a capacitor bank on its DC bus into a ramp, which then powers the bridge in the DRSSTC. Rough schematic of the power end:
Nothing special - just a synchronous buck/class-D amplifier. Q1 and Q2, which are IGBT modules, chop up the DC input, and L1 and C3 form a low-pass filter which turns the square wave back into a DC voltage. Q2 is essential because it allows the output capacitor to be discharged rapidly. C1, C2, R1, R2, D1, D2 form RCD snubbers on the bricks to keep them nice and cool.
Bricks need beefy gate drives, especially important here since we are hard switching:
The controller is just a microcontroller (currently an Mbed, but soon to be an STM32F4). The built-in ADC is used to compare the output voltage to two thresholds, a lower bound and an upper bound. If the output is lower than the lower bound, the micro turns on the high side, and if its higher than the upper bound, it turns on the low side (hysteresis control/delta modulation/bang-bang control/cycle-by-cycle limiting). It remains to be seen whether the naive software-only implementation can track the Tesla coil load quickly enough regulate properly...
And finally, pictures of all this in real life:
EDIT 3/23/2012: damn I fail at designing RCD snubbers. Schematic updated.