GATE EC 2025 Set 1 — Question 37
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumRouth-Hurwitz CriterionStability AnalysisControl Systems
Control Systems → Stability Analysis → Routh-Hurwitz Criterion
Last updated
Question
Consider the polynomial . Let be defined as follows.
is the number of roots of with negative real parts.
is the number of roots of that are purely imaginary.
is the number of roots of with positive real parts.Which one of the following options is correct?
is the number of roots of with negative real parts.
is the number of roots of that are purely imaginary.
is the number of roots of with positive real parts.Which one of the following options is correct?
Correct answer
(A) L = 2, I = 2, and R = 1
Solution
To find the location of the roots of , we construct the Routh-Hurwitz table:A row of zeros occurs at . We form the auxiliary equation from the row:
.
Thus, there are purely imaginary roots.To complete the table, we replace the row with the coefficients of :The first column of the Routh table is: .
There is only one sign change (from to ).
Therefore, the number of roots in the right-half plane is .The total number of roots is 5. The number of roots in the left-half plane is .
So, . Correct option is (A).
.
Thus, there are purely imaginary roots.To complete the table, we replace the row with the coefficients of :The first column of the Routh table is: .
There is only one sign change (from to ).
Therefore, the number of roots in the right-half plane is .The total number of roots is 5. The number of roots in the left-half plane is .
So, . Correct option is (A).
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 …