stability criteria - why include unit circle in z plane?

[nabeel_uet]

stability criteria

why it is necessary that region of convergence of any stable system must include unit circle in z plane?

 

[xulfee]

stability criteria

to make ur feedback -ve,if it is not going to include unit circle u may've +ve feedback,which make ur system unstable

 

[LvW]

Re: stability criteria

why it is necessary that region of convergence of any stable system must include unit circle in z plane?

In the s domain all poles of a stable system must be located in the left half plane (neg. real part).
Based on the definition of the variable z the left half plane of the frequency variable s is transferred into the inner region of the unit circle in the z domain.