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Pole and zero at the same point

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iVenki

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Is it possible to have poles and zeroes at the same point?
 

They will cancel, but this is not reason for impossibility.
Imagine a system consisting in two cascaded, not coupled parts. The first one can have a pole at some location, and the other one can have a zero at the same location.
This type of cancellation is usual in compensation for control systems.
Regards

Z
 

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