I want to know how many the compensation technology for stability for power IC. For example, miller compensation and slope compensation and so on. Is there any other compensation technology for stability?
lead lag compensation. for 2-stage opamp with first stage cascode, there is a modified miller compensation, refer to razavi's book.
for multi-stage opamp, there r lots of compensation techniques, try to search in IEEE. i remember a professor in hongkong, called T.K. Mok had some good papers on it.
slope comp is for current mode ic's only. better to start with voltage mode (simply comparing error voltage to a ramp) because it is more clear.
so there are a few kinds of compensation. if your output cap has a lot of ESR, you get a free low-frequency zero and can use type 2 compensation (1 pole, 1 zero). if you have a low-esr output cap, you need type 3 - (one pole two zeros)
Looks like this circuit leg is used to minimise the op-amp gain at higher frequency to improove the overall closed-loop stability. But also this could be done to introduse a supplementary pole (zero) in the transfer function. It depends on a concrete circuit.