Why does Z≠0 correspond to instability?
From MurrayWiki
First recall some definitions:
- the "loop transfer function" is
- the closed loop system is described by
- Failed to parse (lexing error): Z=#\text{RHP zeros of}1+L(s)
So we see that if a point is a zero of , then it is a pole of the closed-loop system. Now, if that pole lies in the right half-plane, then the closed-loop system will be unstable. Thus if the function has any RHP zeros, the closed loop system around the loop transfer function is unstable.