The technique suggested in this paper of measuring the linear
amplifier output current via current shunts in the supply rails has
been previously reported [5]. In that work, those two currents
are re-combined to create the one controlling signal for the class
D stage.
The operation with a switching deadband around zero output
has also been successfully demonstrated [6], but with a complex
unipolar switching full bridge stage, and two linear amplifiers
for the two ends of the bridge-tied load.