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Electronics and Communication Engineering (ECE) Exam  >  Electronics and Communication Engineering (ECE) Tests  >  GATE ECE (Electronics) Mock Test Series 2025  >  Test: State Variable Analysis - 1 - Electronics and Communication Engineering (ECE) MCQ

Test: State Variable Analysis - 1 - Electronics and Communication Engineering (ECE) MCQ


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10 Questions MCQ Test GATE ECE (Electronics) Mock Test Series 2025 - Test: State Variable Analysis - 1

Test: State Variable Analysis - 1 for Electronics and Communication Engineering (ECE) 2024 is part of GATE ECE (Electronics) Mock Test Series 2025 preparation. The Test: State Variable Analysis - 1 questions and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus.The Test: State Variable Analysis - 1 MCQs are made for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: State Variable Analysis - 1 below.
Solutions of Test: State Variable Analysis - 1 questions in English are available as part of our GATE ECE (Electronics) Mock Test Series 2025 for Electronics and Communication Engineering (ECE) & Test: State Variable Analysis - 1 solutions in Hindi for GATE ECE (Electronics) Mock Test Series 2025 course. Download more important topics, notes, lectures and mock test series for Electronics and Communication Engineering (ECE) Exam by signing up for free. Attempt Test: State Variable Analysis - 1 | 10 questions in 30 minutes | Mock test for Electronics and Communication Engineering (ECE) preparation | Free important questions MCQ to study GATE ECE (Electronics) Mock Test Series 2025 for Electronics and Communication Engineering (ECE) Exam | Download free PDF with solutions
Test: State Variable Analysis - 1 - Question 1
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Which one of the following information is necessary to formulate the problem of control systems optimization?

Test: State Variable Analysis - 1 - Question 2
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For arbitrary pole placement, the following combination is necessary.

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Test: State Variable Analysis - 1 - Question 3
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For a linear time invariant system, an optimal controller can be designed if

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An optimal controller for an LTI system can be designed provided the system is both controllable and observable

Test: State Variable Analysis - 1 - Question 4
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The eigen values of linear system are the location of
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Eigen value are given by | sI - A | = 0, which is the location of poles.

Test: State Variable Analysis - 1 - Question 5
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If the system matrix of a linear time invariant continuous system is given by 


Its characteristic equation will be given by
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Characteristic equation is

or, s2 + 5s + 2 = 0

Test: State Variable Analysis - 1 - Question 6
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​The state-variable description of a linear autonomous system is is a two-dimensional state vector and A is a matrix given by 


The poles of the system are located at 
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Poles of given system are given by

Test: State Variable Analysis - 1 - Question 7
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Assertion (A): The eigen values of a linear continuous-data time invariant system controls the stability of the system.
Reason (R): The roots of the characteristic equation are the same as the eigen values of system matrix A of the state equations.
Test: State Variable Analysis - 1 - Question 8
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The vector matrix differential equation of a system is given by 

The state transition matrix of the system is
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We have:



Test: State Variable Analysis - 1 - Question 9
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The system matrix of a continous time system is given by:

​The characteristic equation is
Detailed Solution for Test: State Variable Analysis - 1 - Question 9

The characteristic equation | sI - A | = 0.


Now, | sI - A | = 0
or, (s + 5) [(s + 5)2 + 0] + 1 (0 - 0) + 0 = 0
or, (s + 5)3 = 0 or s3 + 15s2 + 75s + 125 = 0

Test: State Variable Analysis - 1 - Question 10
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A system is described by the following equations:

The transfer function of the system is
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Transfer function is given by

Given,

and

Now, 



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State Variable Analysis - 1 MCQs with Answers

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