Question

Assertion (A): The stability of the system is assured if the ROC includes the unit circle in z-plane.

Reason (R): For a causal stable system all the poles should be outside the unit circle in the z-plane.

(a) Both A and R are true and R is the correct explanation of A

(b) Both A and R are true bit R is NOT the correct explanation of A

(c) A is true but R is false

(d) A is false but R is true

I have been asked this question during an internship interview.

The doubt is from Difference Equations topic in division Digital Control Systems of Control Systems

Answer 1

Correct answer is (c) A is true but R is false

For explanation I would say: A causal system LTI system is stable if and only if all of poles of H(z) lie inside the unit circle.