Why does Z≠0 correspond to instability?

From MurrayWiki

First recall some definitions:

  • the "loop transfer function" is L(s) = P(s)C(s)
  • the closed loop system is described by \frac{L(s)}{1+L(s)}
  • Z = #RHP zeros of 1 + L(s)

So we see that if a point is a zero of 1 + L(s), 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 1 + L(s) has any RHP zeros, the closed loop system around the loop transfer function is unstable.

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

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