Test: State Space System Analysis

# Test: State Space System Analysis

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## 10 Questions MCQ Test Signals and Systems | Test: State Space System Analysis

Test: State Space System Analysis for Electrical Engineering (EE) 2023 is part of Signals and Systems preparation. The Test: State Space System Analysis questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: State Space System Analysis MCQs are made for Electrical Engineering (EE) 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: State Space System Analysis below.
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Test: State Space System Analysis - Question 1

### The state space or the internal description of the system still involves a relationship between the input and output signals, what are the additional set of variables it also involves?

Detailed Solution for Test: State Space System Analysis - Question 1

Explanation: Although the state space or the internal description of the system still involves a relationship between the input and output signals, it also involves an additional set of variables, called State variables.

Test: State Space System Analysis - Question 2

### State variables provide information about all the internal signals in the system.

Detailed Solution for Test: State Space System Analysis - Question 2

Explanation: The state variables provide information about all the internal signals in the system. As a result, the state-space description provides a more detailed description of the system than the input-output description.

Test: State Space System Analysis - Question 3

### Which of the following gives the complete definition of the state of a system at time n0?

Detailed Solution for Test: State Space System Analysis - Question 3

Explanation: We define the state of a system at time n0 as the amount of information that must be provided at time n0, which, together with the input signal x(n) for n≥n0 determines output signal for n≥n0.

Test: State Space System Analysis - Question 4

From the definition of state of a system ,the system consists of only one component called memory less component.

Detailed Solution for Test: State Space System Analysis - Question 4

Explanation: According to the definition of state of a system, the system consists of two components called memory component and memory less component.

Test: State Space System Analysis - Question 5

If we interchange the rows and columns of the matrix F, then the system is called as:

Detailed Solution for Test: State Space System Analysis - Question 5

Explanation: The transpose of the matrix F is obtained by interchanging its rows and columns, and it is denoted by FT. The system thus obtained is known as Transposed system.

Test: State Space System Analysis - Question 6

A single input-single output system and its transpose have identical impulse responses and hence the same input-output relationship.

Detailed Solution for Test: State Space System Analysis - Question 6

Explanation: If h(n) is the impulse response of the single input-single output system, and h1(n) is the impulse response of the transposed system, then we know that h(n)=h1(n). Thus, a single input-single output system and its transpose have identical impulse responses and hence the same input-output relationship.

Test: State Space System Analysis - Question 7

A closed form solution of the state space equations is easily obtained when the system matrix F is:

Detailed Solution for Test: State Space System Analysis - Question 7

Explanation: A closed form solution of the state space equations is easily obtained when the system matrix F is diagonal. Hence, by finding a matrix P so that F1=PFP-1 is diagonal, the solution of the state equations is simplified considerably.

Test: State Space System Analysis - Question 8

What is the condition to call a number λ is an Eigen value of F and a nonzero vector U is the associated Eigen vector?

Detailed Solution for Test: State Space System Analysis - Question 8

Explanation: A number λ is an Eigen value of F and a nonzero vector U is the associated Eigen vector if
FU= λU
Thus, we obtain (F- λI)U=0.

Test: State Space System Analysis - Question 9

The determinant |F- λI|=0 yields the characteristic polynomial of the matrix F.

Detailed Solution for Test: State Space System Analysis - Question 9

Explanation: We know that (F- λI)U=0
The above equation has a nonzero solution U if the matrix F- λI is singular, which is the case if the determinant of (F- λI) is zero. That is, |F- λI|=0.
This determinant yields the characteristic polynomial of the matrix F.

Test: State Space System Analysis - Question 10

The parallel form realization is also known as normal form representation.

Detailed Solution for Test: State Space System Analysis - Question 10

Explanation: The parallel form realization is also known as normal form representation, because the matrix F is diagonal, and hence the state variables are uncoupled.

## Signals and Systems

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## Signals and Systems

32 videos|76 docs|63 tests