Pole Location in z-Plane

Correct Answer

A — is stable

Concept and Reasoning

The characteristic equation factors as z(z−0.9)(z+0.9)=0. All three poles have magnitude less than 1, so the discrete-time system is asymptotically stable.

Calculation / Key Relation

Poles: z=0, ±0.9

stable if |z|<1

Exam Takeaway

Discrete-time stability is checked against the unit circle.

Common Mistake

Do not apply the continuous-time left-half-plane criterion to z-plane poles.