This set of Control Systems Multiple Choice Questions & Answers (MCQs) focuses on “Difference Equations”.

1. Difference equation is used in :

a) Discrete time analysis

b) Continuous time analysis

c) Digital analysis

d) None of the mentioned

2. Difference equation in discrete systems is similar to the _____________ in continuous systems.

a) Difference equation

b) Differential equation

c) Quadratic equation

d) None of the mentioned

3. Difference equation model results in:

a) Sampled-data systems

b) Numerical analysis of continuous time systems

c) Continuous time feedback systems

d) Both a and b

4. Difference equation solution yields at the sampling instants only:

a) True

b) False

5. 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

6. If X(z) =(z+z^{-3})/(z+z^{-1}), then x(n) series has:

a) Alternate 0s

b) Alternate 1s

c) Alternate 2s

d) Alternate -1s

7. Difference equation technique for higher order systems is used in:

a) Laplace transform

b) Fourier transform

c) Z-transform

d) None of the mentioned

8. The poles of a digital filter with linear phase response can lie

a) Only at z =0

b) Only on the unit circle

c) Only inside the unit circle but not at z =0

d) On the left side of Real (z) =0 line

9. 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

10. Assertion (A): For the rational transfer function H(z) to be causal, stable and causally invertible, both the zeroes and the poles should lie within the unit circle in the z-plane.

Reason (R): For a rational system, ROC is bounded by poles

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