Question

1.In your own words, why does the location of poles define stability?

2.In your own words, why does the location of zeros control the magnitude of the response?

Answer 1

1) For a stable system , all poles must lie on the left hand side of the s plane. Right hand side poles cause instability. This is because left hand side poles give rise to decaying exponentials that converge to a finite value while right hand side poles produce growing exponentials which tend to have infinite values and never converge. So system becomes unstable.

2) The location of zeroes determine the time domain paramters like rise time, peak time, overshoot, delay time and settling time and thus control magnitude of response.