Can someone please explain, provide a link or cite a book where the properties of the zeros for continuous and discrete time systems are explained? I know that the zeros are the frequencies where the numerator of a transfer function becomes zero.

$$

H(s) = \frac{A(s)}{B(s)}

$$

But I would like to know what role the location plays in the pole-zero plot?

All I can find are pole-zero plots and that basically the poles define the system stability and time response.

However, what are the zeros "doing"?

What happens if the zeros are in the right or left half plane?

Are the zeros describing the damping or also stability?

Here is a link to a pdf of MIT explaining the pole zeros. However, I am missing details about zeros.

## Best Answer

1)zeros with positive real part give a negative phase contribution, reducing the phase margin (which is bad) thus limits the performance of the system.

2)Time delay in the system can also be approximated as a zero with positive real part (see first order Pade approximation 1), similar effect as previous point.

3)Blocking property of zeros, If you have a transfer function with a zero in the right hand plane, and an input tuned to that zero, then the output is at 0 for any time t. Example: Proof for blocking property of zeros:3