Another powerful tool which allows one to evaluate the behaviour / stability of the system in closed loop mode as the loop (feedback) gain varies, is the Root Locus Method. The user can observe how the closed loop pole positions change as the open loop gain is adjusted.

See http://en.wikipedia.org/wiki/Root_locus

 

If you like you can plot Y(s)/X(s) but by plotting β*H(s) one can see if the system is stable immediatley. If the phase of β*H(s) is greater than 180 then the system is unstable.

 

Alright, thanks a lot for all the explanations. I really learned a lot from you guys...