GATE EE 2014 Set 1 — Question 27
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Control Systems → Stability Analysis → Routh-Hurwitz Criterion
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Question
In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of
Correct answer
(B) imaginary roots
Solution
A row of zeros in the Routh-Hurwitz array indicates the existence of an auxiliary polynomial, which occurs when roots are located symmetrically about the origin. This includes pairs of purely imaginary roots (), pairs of real roots of opposite sign (), or complex conjugate pairs symmetric about the origin. In the context of standard control systems problems, this condition is most commonly associated with the presence of imaginary roots.
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