Question: I have been trying to figure out how the following circuit works and what it might be good for without any luck so far. 

What might the transfer function be?

Is there a way that analysis can be applied generally to many such loops inside each other ?

(for analysis purpose exact op amp type does not matter, and may be considered ideal)

[![op amp multi feedback](https://i.stack.imgur.com/6zAdU.jpg)](https://i.stack.imgur.com/6zAdU.jpg)

Upon recommendation, i tried the delta-star transformation, and came up with conclusion that n loops can be simplified to the circuit below:

[![op amp feedback transformed](https://i.stack.imgur.com/VgPIm.jpg)](https://i.stack.imgur.com/VgPIm.jpg)

This looks like inverting op amp but there is one resistor left from the last transformation connected to inverting input. Is this correct, or am I missing something ?

Answer: 
The [IR2110](https://www.infineon.com/dgdl/ir2110.pdf?fileId=5546d462533600a4015355c80333167e) is designed to supply +/-2A to drive the gate of your output devices.

You have an asymmetric drive caused by the 47 Ohm and diode across it. 

You have not specified what 2VM1 is, but assuming it's no more than a 15V supply your maximum gate drive current is about 0.3A during turn on. During turn off you may be exceeding the gate drive capability of the IR2110 since you then have 47 Ohm with whatever the effective Vf slope resistance of the diode is (along with a 0.8-0.9V offset). 

I'd suggest you could remove D2, 3, 5, 6 and replace the 47 Ohm with 10 Ohm resistors. This will make the turn on/off delays **the same** which is important. With a 15V VCC that will give you 1.5A charge/discharge current.
You have problem with charging the bootstrap capacitor cause its charging thru 2l at very high frequency he will never charge for needed value.