GATE EE 2025 Set 1 — Question 41
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Control Systems → Stability Analysis → Routh-Hurwitz Criterion
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Question
Let . Then the closed-loop system shown in the figure below, is
Correct answer
(B) unstable for all K 2.
Solution
The characteristic equation of the closed-loop system is .
Substituting :
For stability, all coefficients of the characteristic equation must be positive.
Substituting :
For stability, all coefficients of the characteristic equation must be positive.
1.
2.
Thus, the system is stable for and unstable for . Option (B) correctly states it is unstable for all .Continue learning with Success Tracker
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