engineering recuitment GATE IN Test Series 2023-24 Mock Test Control Systems State Space Analysis State Space Representation
A certain linear, time-invariant system has the state and output representation shown below:
\(\begin{pmatrix} \dot x_1 \\\ \dot x_2 \end{pmatrix} = \begin{pmatrix} -3 & 1 \\\ 0& -2 \end{pmatrix} \begin{pmatrix} x_1 \\\ x_2 \end{pmatrix} + \begin{pmatrix} 1 \\\ 0 \end{pmatrix} \rm u\)
\(y = \begin{pmatrix} 1 & 1 \end{pmatrix} \begin{pmatrix} x_1 \\\ x_2 \end{pmatrix} \)
For input = 0, the initial condition, such that y(t) = Ae-3t for t > 0 is _____.
1
x1 (0) = A, x2(0) = 0
2
x1(0) = 0, x2(0) = A
3
x1(0) = A, x2(0) = A
4
x1(0) = 0, x2(0) = 0