Q109
Let the state-space representation of an LTI system be \[ X ^ \](t) = AX(t) + Bu(t), y(t) = CX(t) + Du(t) where A, B, C are matrices, D is a scalar, u(t) is the input to the system, and y(t) is its output. Let B = [0 0 1]T and D = 0. Which one of the following options for A and C will ensure that the transfer function of this LTI system is \[H ( s ) = 1s^3 + 3s^2 + 2s + 1\]
Let the state-space representation of an LTI system be (t) = AX(t) + Bu(t), y(t) = CX(t) + Du(t) where A, B, C are matrices, D is a scalar, u(t) is the input to the system, and y(t) is its output. Let B = [0 0 1]T and D = 0. Which one of the following options for A and C will ensure that the transfer function of this LTI system is
A.
A = \left[ {\begin{array}{*{20}{c}}
0&1&0\\
0&0&1\\
{ - 3}&{ - 2}&{ - 1}
\end{array}} \right]{\rm{ and }} \,C = \left[ {0\,\,\,0\,\,\,1} \right]
B.
A = \left[ {\begin{array}{*{20}{c}}
0&1&0\\
0&0&1\\
{ - 1}&{ - 2}&{ - 3}
\end{array}} \right]{\rm{ and }} \,C = \left[ {0\,\,\,0\,\,\,1} \right]
C.
A = \left[ {\begin{array}{*{20}{c}}
0&1&0\\
0&0&1\\
{ - 1}&{ - 2}&{ - 3}
\end{array}} \right]{\rm{ and }} \,C = \left[ {1\,\,\,0\,\,\,0} \right]
AnswerD.
A = \left[ {\begin{array}{*{20}{c}}
0&1&0\\
0&0&1\\
{ - 3}&{ - 2}&{ - 1}
\end{array}} \right]{\rm{ and }} \,C = \left[ {1\,\,\,0\,\,\,0} \right]
Answer: Option C
Solution
Answer: Option C
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