Does a RHP zero imposes some limitation in the time domain?

I am studying control systems and I have seen that a non-minimum phase zero imposes a limitation on the bandwidth, which is that the bandwidth has to be lower than the frequency which is half the frequency of the RHP pole.

I have also seen that it imposes in the step response an undershoot, but as far as I know there are no other influences of RHP zero in the time domain.

Does a RHP zero impose any other limitation in the time domain?

• For example, if I have a RHP zero at $s=1$, does it change something if I plot the step response starting at $t=0$ or at $t=5$? Thanks in advance. – J.D. Feb 12 '20 at 15:33