engineering recuitment ISRO Scientist Electronics Mock Test Control Systems State Space Analysis State Transition Matrix
The zero-input response of a system given by the state-space equation.
\(\left[ {\begin{array}{*{20}{c}} {{{\dot x}_1}}\\ {{{\dot x}_2}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 1&0\\ 1&1 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}} \end{array}} \right]\) and \(\left[ {\begin{array}{*{20}{c}} {{x_1}\left( 0 \right)}\\ {{x_2}\left( 0 \right)} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 1\\ 0 \end{array}} \right]\) is1
\(\left[ {\begin{array}{*{20}{c}} t\\ {t{e^t}} \end{array}} \right]\)
2
\(\left[ {\begin{array}{*{20}{c}} {{e^t}}\\ t \end{array}} \right]\)
3
\(\left[ {\begin{array}{*{20}{c}} {{e^{-t}}}\\ t \end{array}} \right]\)
4
\(\left[ {\begin{array}{*{20}{c}} {{e^t}}\\ {t{e^t}} \end{array}} \right]\)