engineering recuitment GATE ECE 2023-24 Test Series Control Systems State Space Analysis State Transition Matrix
The state transition matrix is given by
\({e^{At}} = \left[ {\begin{array}{*{20}{c}} {{e^{ - t}}}&{2\left( {a - b} \right)}\\ 0&{{a^2}{e^{ - 2t}}} \end{array}} \right],\;a > 0\)
The state matrix of system x[t] when x[0] = [1 1]T is ____
1
\(\left[ {\begin{array}{*{20}{c}} { - {e^t}}\\ {{e^{ - 2t}}} \end{array}} \right]\)
2
\(\left[ {\begin{array}{*{20}{c}} {{e^{ - t}}}\\ {{e^{ - 2t}}} \end{array}} \right]\)
3
\(\left[ {\begin{array}{*{20}{c}} { - {e^{ - t}}}\\ { - {e^{ - 2t}}} \end{array}} \right]\)
4
\(\left[ {\begin{array}{*{20}{c}} {{e^{ - t}}}\\ { - {e^{ - 2t}}} \end{array}} \right]\)