Prove the stability properties of z-transform

1. How do you check stability in Z-transform?
2. What is the use of stability in Z-transform?

How do you check stability in Z-transform?

ondition of stability is Z-domain is, [H(Z) < ∞ when evaluated on unit circle. Equation (3.7. 6) gives the condition of stability in Z domain. This condition requires that, unit circle must be present in the ROC of H(Z).

What is the use of stability in Z-transform?

The stability of a system can also be determined by knowing the ROC alone. If the ROC contains the unit circle (i.e., |z| = 1) then the system is stable. In the above systems the causal system (Example 2) is stable because |z| > 0.5 contains the unit circle.