GATE EC 2016 Set 1 — Question 29
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+1 / -0.33EasyRouth-Hurwitz CriterionStability AnalysisControl Systems
Control Systems → Stability Analysis → Routh-Hurwitz Criterion
Last updated
Question
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.
| Inference | Property |
|---|---|
| X: The system is stable … | P: … when all elements are positive |
| Y: The system is unstable … | Q: … when any one element is zero |
| Z: The test breaks down … | R: … when there is a change in sign of coefficients |
Correct answer
(D) X→P, Y→R, Z→Q
Solution
According to the Routh-Hurwitz stability criterion:
1.A system is stable if all elements in the first column of the Routh table are positive (X P).
2.A system is unstable if there are sign changes in the first column. The number of sign changes equals the number of roots in the right-half -plane (Y R).
3.The Routh test breaks down if any element in the first column is zero, requiring special procedures like replacing zero with a small or using the auxiliary polynomial (Z Q).
Thus, the correct matching is X P, Y R, Z Q, which corresponds to option (D).Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE EC question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Stability Analysis
2026 Set 1 Q11Consider the differential equation , with…2026 Set 1 Q19A control system is shown in the Figure. Which option represents the correct transfer function of…2026 Set 1 Q40For the control system shown in the Figure, the transfer function of a plant,…2026 Set 1 Q41The state and output equations for a control system are:…2026 Set 1 Q59Consider the unity negative feedback control system shown in the Figure. The value of gain …