Does pole zero cancellation happen and is it useful?
It is generally a bad idea to cancel unstable poles or zeros because for this to work it would need to be exact; for real systems, we almost never know exactly where a pole or zero is because our model can never be good enough. However, for robust performance considerations, it is sometimes useful to cancel a stable pole or zero. Chapter 12 of Astrom and Murray talks more about this.
--Julia Braman 19:03, 3 November 2008 (PST)