Hi everyone !

Currently, I am studying Control Theory and I believe it is a fascinating field ! I still have a lot to learn !
Anyway, I have a question to ask because I am not very sure.
I have just learned about Pole Placement. I know the key is to find a gain K in order to meet my specifications and change system's behavior by what I desire. In order to do that, it is necessary to check a criterion: Kalman's Criterion (to know if my system is controllable and if I can place my pole as I want).

My first question: Imagine a system that is initially no stable (with positive eigenvalues for example) .
Can I assume it does not check Kalman's Criterion ?
Can I do a Pole Placement to make it stable ?
Are there other methods to make a system stable ?

My second question: I am working with linear system. However, I think in life, real systems are not necessarily linear.
Can I do a pole placement in a nonlinear system ?

Thank you for your help !
Have a nice day ! Small Bio