GATE 2016 EC – Question 29
Match the inferences X, Y, and Z, about a system, to the corresponding properties of the elements of first column in Routh's Table of the system characteristic equation.
X: The system is stable ...
Y: The system is unstable ...
Z: The test breaks down ...
P: ... when all elements are positive
Q: ... when any one element is zero
R: ... when there is a change in sign of coefficients
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Correct answer: (D) XP, YR, ZQ
Explanation
In Routh's test the system is stable when all the elements of the first column are positive. It is unstable when the sign changes in the first column, and the number of sign changes is the number of right-half plane roots. The test breaks down when an element of the first column is zero, so the array cannot be completed in the usual way. That matches X with P, Y with R and Z with Q.