engineering recuitment ISRO Scientist Electronics Mock Test Control Systems State Space Analysis State Transition Matrix
What is the state-transition matrix Φ{t) of the following system?
\(\begin{bmatrix}\dot {x_1}\\\ \dot {x_2}\end{bmatrix}=\begin{bmatrix}0&1\\\ -2&-3\end{bmatrix}\begin{bmatrix} {x_1}\\\ {x_2}\end{bmatrix}\)
1
\(\Phi(t)=\begin{bmatrix}e^{-t}-e^{-2t}&e^{-t}-e^{-2t}\\\ -2e^{-t}+2e^{-2t} &-e^{-t}+2e^{-2t}\end{bmatrix}\)
2
\(\Phi(t)=\begin{bmatrix}2e^{-t}-e^{-2t}&e^{-t}-e^{-2t}\\\ -2e^{-t}+2e^{-2t} &-e^{-t}+2e^{-2t}\end{bmatrix}\)
3
\(\Phi(t)=\begin{bmatrix}2e^{-t}-e^{-2t}&e^{-t}-e^{-2t}\\\ -e^{-t}+e^{-2t} &-e^{-t}+e^{-2t}\end{bmatrix}\)
4
\(\Phi(t)=\begin{bmatrix}2e^{-t}-2e^{-2t}&2e^{-t}-e^{-2t}\\\ -2e^{-t}+2e^{-2t} &-2e^{-t}+2e^{-2t}\end{bmatrix}\)