# Difference between revisions of "Why does Z≠0 correspond to instability?"

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[[User:Hines|George Hines]] 17:12, 12 November 2007 (PST) | [[User:Hines|George Hines]] 17:12, 12 November 2007 (PST) | ||

− | [[Category: | + | [[Category: CDS 101/110 FAQ - Lecture 7-1]] |

+ | [[Category: CDS 101/110 FAQ - Lecture 7-1, Fall 2007]] |

## Latest revision as of 01:12, 13 November 2007

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)