What does it mean that a zero is slow? I am studying control systems, and have encountered the definition of a slow zero. I am searching on internet and in books, but I don't understand the meaning this. I know that if a zero is too slow, it introduces a resonance peak and an overshoot in the step response, but what is a slow zero?
I thought it was a zero close to the imaginary axis in the root locus, so a zero at low frequencies, but I am not sure, since I cannot find a definition.
I know that a pole that is close from the imaginary axis settles quicker than a pole far from the imaginary axis. But I did some simulations in Matlab, and using a lead compensator, I have seen that if I decrease frequency of the zero in the lead compensator, the overshoot in the step response increases.

Here, the lead compensators I have used are as below.
lead = (1+10*0.05*s)/((1+0.05*s));          %red line
lead_2 = (1+30*0.083*s)/((1+0.083*s));      %blu line
lead_3 = (1+50*0.083*s)/((1+0.083*s));      %green line

Can somebody help me?
Again I refer you to the Murray's book. Which is free by the way

http://www.cds.caltech.edu/~murray/books/AM08/pdf/fbs-limits_18Aug2019.pdf

From the book "Furthermore a zero is said to be “slow” if its magnitude is smaller
than the intended closed loop bandwidth."