# Why does Z≠0 correspond to instability?

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First recall some definitions:

- the "loop transfer function" is
- the closed loop system is described by
- Z = #RHP zeros of

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.

George Hines 17:12, 12 November 2007 (PST)