Routh-Hurwitz MCQs

Practice Routh-Hurwitz MCQs with four options, answers and explanations for focused Electronics & Telecommunication Engineering revision.

Question 1

Control SystemsRouth-Hurwitz

The Routh-Hurwitz criterion is primarily used to determine?

AAbsolute stability without explicitly calculating all roots
BOnly steady-state gain
COnly system bandwidth
DInput signal amplitude

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Correct Answer: A. Absolute stability without explicitly calculating all roots

Explanation: The Routh-Hurwitz criterion determines how many characteristic roots lie in the right half-plane and hence assesses absolute stability.

Reference: Standard control systems: routh-hurwitz

Question 2

Control SystemsRouth-Hurwitz

For a polynomial with all positive coefficients, positivity of coefficients alone is?

AAlways sufficient for stability
BNecessary but not generally sufficient for Hurwitz stability
CNever relevant
DSufficient only for every fourth-order system

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Correct Answer: B. Necessary but not generally sufficient for Hurwitz stability

Explanation: For a Hurwitz polynomial, coefficients must satisfy necessary sign conditions, but positive coefficients alone do not guarantee all roots lie in the left half-plane.

Reference: Standard control systems: routh-hurwitz

Question 3

Control SystemsRouth-Hurwitz

At K=6 for s³+2s²+3s+K, the system is at the?

AStability boundary
BAlways strictly stable
CAlways overdamped
DOrigin with three repeated poles

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Correct Answer: A. Stability boundary

Explanation: At K=6, a Routh first-column element becomes zero and a conjugate pair lies on the imaginary axis, marking the stability boundary.

Reference: Standard control systems: routh-hurwitz

Question 4

Control SystemsRouth-Hurwitz

The number of sign changes in the first column of a Routh array equals the number of roots in the?

ALeft half-plane
BRight half-plane
COrigin only
DImaginary axis only

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Correct Answer: B. Right half-plane

Explanation: Routh's criterion states that first-column sign changes equal the number of roots in the right half of the s-plane.

Reference: Standard control systems: routh-hurwitz

Question 5

Control SystemsRouth-Hurwitz

The characteristic polynomial s²+4s+8 is stable because its second-order coefficients are?

AAll positive
BAll negative
CAlternating in sign
DZero

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Correct Answer: A. All positive

Explanation: For a second-order polynomial s²+a1s+a0, positive a1 and a0 imply both roots have negative real parts.

Reference: Standard control systems: routh-hurwitz

Question 6

Control SystemsRouth-Hurwitz

For the cubic polynomial s³+2s²+3s+K, the Routh stability condition for positive K includes?

AK>6
B0<K<6
CK<0 only
DK=6 only

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Correct Answer: B. 0<K<6

Explanation: The cubic Routh first column is 1, 2, (6-K)/2, K. All must be positive, giving 0<K<6.

Reference: Standard control systems: routh-hurwitz