Class AB control is reached through a translinear loop. Control transistors, np3 and pp15, are driven by a N mirror and a P mirror. Diode connected transistor set the bias point of control transistors.
Notice that N and P mirrors are complimentary, that is, when one of them increases the current, the other one reduces its current.
So, for exmaple, when the N mirror puts more current, source of np3 goes down making the N-type output transistor to shut off. On the other hand, the P mirror puts less current, which cuts pp7 and then its source node gets high impedance. This allows the drain of np3 to go down, pushing from the gate of the P-type output transistors, making it to conduct more current.
The dual behavior occurs when the N mirror reduces its current and the P mirror putsq more current through the controls transistors.
Compensation is Miller-like. You must determine the capacitors in both cases when the N output transistor is on (P off) and when the P is on (N off).