Consider the following statements regarding a system y=f(x1) 1. f(x1+x2)=f(x1)+f(x2) 2. f[x(t+T)]=f[x(t)]+f[x(T)] 3.f(Kx)=Kf(x). Of these statements

1.  1,2 and 3 are correct

2.  2 and 3 are correct

3.  1 and 2 are correct

4.   1 and 3 are correct

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4
Correct Answer :

1 and 3 are correct


Explanation :
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Which one of the following system is completely state controllable

1.  

2.  

3.  

4.  

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Explanation :
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For φ(s)=, The coefficient matrix A is

1.  

2.  

3.  

4.  

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Correct Answer :


Explanation :
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Laplace transform of is

1.  

2.  

3.  

4.  

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4
Correct Answer :


Explanation :
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A system is described by the state equation X=AX+BU. The output is given by Y=CX, where A=, B=, C=[1 0] Transfer function G(s) of the system is

1.  

2.  

3.  

4.  

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Correct Answer :


Explanation :
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The Laplace transform of is given by

1.  

2.  

3.  

4.  

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Correct Answer :


Explanation :
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The matrix of any state-space equations for the transfer function C(s)/R(s) of the system shown below in the figure is

1.  

2.  

3.  [-1]

4.  [3]

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4
Correct Answer :

[-1]


Explanation :
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Given the homogeneous state-space equation X=X The steady state value of Xss=X(t), the initial state value of X(0)=[10-10]T, is

1.  

2.  

3.  

4.  

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4
Correct Answer :


Explanation :
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If , then is equal to

1.  

2.  

3.  

4.  

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4
Correct Answer :


Explanation :
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The Laplace transform of is

1.  

2.  

3.  

4.  

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4
Correct Answer :


Explanation :
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