Routh Hurwitz Criterion MCQ

1. Consider the following statements with respect to Routh-Hurwitz criterion:

  1. It can be used to determine relative stability.
  2. It is valid only for real coefficients of the characteristic equation.
  3. It is applicable only for non-linear systems.
  4. It does not provide the exact location of closed-loop poles in left or right-half of s-plane.

Which of the above statements are correct?

  1. i, ii and iii only
  2. iii and iv only
  3. i, ii and iv only
  4. i, ii, iii and iv
Answer
Answer. c

2. The first element of each of the rows of a Routh-Hurwitz stability test showed the signs as follows:

Row I II III IV V
Sign + + – + –

Consider the following statements:

  1. The system has three roots in the right-half of s-plane
  2. The system has three roots in the left-half of s-plane.
  3. The system is stable.
  4. The system is unstable.

Which of the above statements about the system are correct?

  1. i and iv
  2. i and iii
  3. ii and iv
  4. ii and iii
Answer
Answer. a

3. Consider the following statements about Routh-Hurwitz criterion:

If all the elements in one row of Routh array are zero, then there are

  1. Pairs of conjugate roots on imaginary axis.
  2. Pairs of equal real roots with opposite sign
  3. Conjugate roots forming a quadrate in the s-plane.

Which of these statements are correct?

  1. i and ii only
  2. i and iii only
  3. ii and iii only
  4. i, ii and iii
Answer
Answer. d

4. Using Routh’s criterion, the number of roots in the right half s-plane for the characteristic equation:

s4 + 2s3 + 2s2 + 3s + 6 = 0 is

  1. two
  2. one
  3. four
  4. three
Answer
Answer. a

5. Consider the following statements regarding Routh-Hurwitz criterion for stability:

  1. Routh-Hurwitz criterion is a necessary and sufficient condition for stability.
  2. The relative stability is dictated by the location of the roots of the characteristic equation.
  3. A stable system is a dynamic system with a bounded response to a bounded input.

Which of the statements given above are correct?

  1. ii and iii
  2. i and ii
  3. i, ii and iii
  4. i and iii
Answer
Answer. c

6. The characteristic equation for a third-order system is

q(s) = a0s3 + a1s2 + a2s + a3 = 0

For the third-order system to be stable, besides that all the coefficients have to be positive, which one of the following has to be satisfied as a necessary and sufficient condition?

  1. a0a1 ≥ a2a3
  2. a1a2 ≥ a0a3
  3. a2a3 ≥ a1a0
  4. a0a3 ≥ a1a2
Answer
Answer. b

7. Consider the following statements:

When all the elements in one row of the Routh’s tabulation are zero then this condition indicates:

  1. one pair of real roots with opposite sign in s-plane
  2. one pair of conjugate roots on the imaginary axis in s-plane
  3. conjugate roots forming a quadrate in s-plane

Which of the statements given below is/are correct?

  1. i only
  2. ii only
  3. i, ii and iii
  4. iii only
Answer
Answer. c

8. While forming a Routh array, the situation of a row of zeros indicates that the system

  1. has asymmetrically located roots
  2. is insensitive to variation in gain
  3. is stable
  4. has symmetrically located roots
Answer
Answer. a