What is a interlaced zero in transfer function?

[skyhj105]

A reading assignment I have read said "By adding a direct feed-through to a
collocated system, the transfer function can be modified from containing
resonant poles followed by interlaced zeros, to zeros followed by interlaced
poles." I don`t konw what this sentence mean. What is the resonant poles followed by interlaced zeros and resonant poles followed by interlaced zeros?
(I know that In feedback system, stability can be determined by location of ploes. And if every pole exists in real negative axis, we can call the system stable.)

 

[Illmatic1]

In this sentence, the "resonant poles followed by interlaced zeros" refers to a transfer function that has a pole at each resonance frequency, followed by a zero at each resonance frequency. This type of transfer function is often used in feedback systems, as it can provide stability (as you mentioned, if all the poles are located in the real negative axis, the system is stable). By adding a direct feed-through to the collocated system, it is possible to modify the transfer function so that the zeros come first, followed by the poles. This results in a different type of transfer function with different characteristics.