Question

Assertion (A): An LTI discrete system represented by the difference equation. y (n+2)-5y(n+1)+6y(n) =x(n) is unstable.

Reason (R): A system is unstable if the roots of the characteristic equation lie outside the unit circle.

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

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

(c) A is true but R is false

(d) A is false but R is false

The question was posed to me in an interview for job.

Enquiry is from Difference Equations topic in portion Digital Control Systems of Control Systems

Answer 1

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

To elaborate: Difference equation is y (n+2)-5 y (n+1) + 6 y (n) =x (n).

Taking z-transform, H (z) =1/ (z-2) (z-3).

The characteristic equation has roots z =2, 3. Since, the characteristic equation has roots outside the unit circle, hence the system is unstable.