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 falseThe question was posed to me in an interview for job.Enquiry is from Difference Equations topic in portion Digital Control Systems of Control Systems

Assertion (A): An LTI discrete system represented by the difference eq

1.	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 falseThe 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» 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.

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