Test: The State Variable Analysis - 3 - Electrical Engineering (EE) MCQ

# Test: The State Variable Analysis - 3 - Electrical Engineering (EE) MCQ

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## 20 Questions MCQ Test GATE Electrical Engineering (EE) Mock Test Series 2025 - Test: The State Variable Analysis - 3

Test: The State Variable Analysis - 3 for Electrical Engineering (EE) 2024 is part of GATE Electrical Engineering (EE) Mock Test Series 2025 preparation. The Test: The State Variable Analysis - 3 questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: The State Variable Analysis - 3 MCQs are made for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: The State Variable Analysis - 3 below.
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Test: The State Variable Analysis - 3 - Question 1

### The state-space representation for a system is The transfer function Y(s) /U(s) is ​ ​ ​

Detailed Solution for Test: The State Variable Analysis - 3 - Question 1

Substituting the values,

Test: The State Variable Analysis - 3 - Question 2

### Determine the state-space representation for the transfer function given in question. Choose the state variable as follows Q.   ​ ​ ​

Detailed Solution for Test: The State Variable Analysis - 3 - Question 2

(s3 + a2s2 + a1s + a0)C(s) = b0R(s)
Taking the inverse Laplace transform assuming zero initial conditions

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Test: The State Variable Analysis - 3 - Question 3

### Determine the state-space representation for the transfer function given in question. Choose the state variable as follows Q.

Detailed Solution for Test: The State Variable Analysis - 3 - Question 3

Fourth order hence four state variable

Test: The State Variable Analysis - 3 - Question 4

A state-space representation of a system is given by

The time response of this system will be​ ​ ​ ​

Detailed Solution for Test: The State Variable Analysis - 3 - Question 4

Test: The State Variable Analysis - 3 - Question 5

Detailed Solution for Test: The State Variable Analysis - 3 - Question 5

Test: The State Variable Analysis - 3 - Question 6

Detailed Solution for Test: The State Variable Analysis - 3 - Question 6

Test: The State Variable Analysis - 3 - Question 7

Consider the system shown in fig.

The controllability matrix is

Detailed Solution for Test: The State Variable Analysis - 3 - Question 7

Test: The State Variable Analysis - 3 - Question 8

Consider the system shown in fig.

The observability matrix is

Detailed Solution for Test: The State Variable Analysis - 3 - Question 8

Test: The State Variable Analysis - 3 - Question 9

Consider the system shown in fig.

The system is

Detailed Solution for Test: The State Variable Analysis - 3 - Question 9

det CM = 0. Hence system is not controllable. det OM = 1. Hence system is observable.

Test: The State Variable Analysis - 3 - Question 10

Consider the system shown in fig.

Q. The controllability matrix for this system is

Detailed Solution for Test: The State Variable Analysis - 3 - Question 10

Test: The State Variable Analysis - 3 - Question 11

Consider the system shown in fig.

The observability matrix is

Detailed Solution for Test: The State Variable Analysis - 3 - Question 11

Test: The State Variable Analysis - 3 - Question 12

Consider the system shown in fig.

Q. The system is

Detailed Solution for Test: The State Variable Analysis - 3 - Question 12

Since the determinant is not zero, the 3 x 3 matrix is nonsingular and system is controllable

The rank of OM is 3. Hence system is observable.

Test: The State Variable Analysis - 3 - Question 13

A state flow graph is shown in fig.

​ ​ ​

Q.The state and output equation for this system is

Detailed Solution for Test: The State Variable Analysis - 3 - Question 13

Test: The State Variable Analysis - 3 - Question 14

A state flow graph is shown in fig.

The system is

Detailed Solution for Test: The State Variable Analysis - 3 - Question 14

det OM = 0. Thus system is not observable

det CM = -1. Thus system is controllable.

Test: The State Variable Analysis - 3 - Question 15

Consider the network shown in fig. The state-space representation for this network is

Detailed Solution for Test: The State Variable Analysis - 3 - Question 15

vc and iL are state variable.

Hence equation are

Test: The State Variable Analysis - 3 - Question 16

For the network shown in fig. The output is

iR(t). The state space representation is

Detailed Solution for Test: The State Variable Analysis - 3 - Question 16

Hence v1 and i3 are state variable.

Test: The State Variable Analysis - 3 - Question 17

Consider the network shown in fig. This system may be represented in state space representation

Q. The state variable may be

Detailed Solution for Test: The State Variable Analysis - 3 - Question 17

Energy storage elements are capacitor and inductor. vC and iL are available in differential form and linearly independent. Hence vC and iL are suitable for state-variable.

Test: The State Variable Analysis - 3 - Question 18

Consider the network shown in fig. This system may be represented in state space representation

Q. If state variable are chosen as in previous question, then the matrix A is

Detailed Solution for Test: The State Variable Analysis - 3 - Question 18

.....(i)
.....(ii)
Solving equation (i) and (ii)

Test: The State Variable Analysis - 3 - Question 19

Consider the network shown in fig. This system may be represented in state space representation

Q. The matrix B is

Detailed Solution for Test: The State Variable Analysis - 3 - Question 19

Test: The State Variable Analysis - 3 - Question 20

Consider the network shown in fig.

Q. The state variable may be

Detailed Solution for Test: The State Variable Analysis - 3 - Question 20

There are three energy storage elements, hence 3 variable. i2 ,i4 and vo are available in differentiated form hence these are state variable.

## GATE Electrical Engineering (EE) Mock Test Series 2025

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## GATE Electrical Engineering (EE) Mock Test Series 2025

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