Feedback MOSFET circuit anaylsis
Not an answer yet, a few hints though







simulate this circuit &ndash; Schematic created using CircuitLab

If you consider just your M1 MOS and its bias source small signal model you may consider \$g_\mathrm{m}v_\mathrm{i}\$ current dependant generator. 

It's open circuit, so the only consistent operation point can be "zero output current" i.e.

$$i_\mathrm{o}=g_\mathrm{m}v_\mathrm{i}=0\quad\Rightarrow\quad v_\mathrm{i}=0$$

So, looking at the input port we have \$(v_\mathrm{i}=0\,;\,i_\mathrm{i}=0)\$ 



In these conditions output voltage could be written as output current over output conductance (zero since it's open circuit)

$$v_\mathrm{o}=-\frac{i_\mathrm{o}}{g_\mathrm{o}}=\frac{0}{0}\;\rightarrow\;\mathrm{undefined}$$

Undefined just means that \$v_\mathrm{o}\$ could be any value. 



Toghether they form one circuit which exhibits zero input voltage and current (sometimes called virtual ground in english speaking countries) and whatever output voltage. 

This is similar to an ideal opamp, the only difference is that our circuit output current has to be zero.
All the above is similar to a nullor

So now @user367640, any idea??