1 1 vote Consider a linear system whose state space representation is $\dot{\mathbf{x}}(t)=\mathbf{A} \mathbf{x}(t)$. If the initial state vector of the system is $\mathbf{x}(0)=\left[\begin{array}{r}1 \\ -2\end{array}\right]$, then the system response is $\mathbf{x}(t)=\left[\begin{array}{r}e^{-2 t} \\ -2 e^{-2 t}\end{array}\right]$ If the initial state vector of the system changes to $\mathbf{x}(0)=\left[\begin{array}{r}1 \\ -1\end{array}\right]$, then the system response becomes $\mathbf{x}(t)=\left[\begin{array}{c}e^{-t} \\ -e^{-t}\end{array}\right]$. The system matrix $\mathbf{A}$ is $\left[\begin{array}{rr}0 & 1 \\ -1 & 1\end{array}\right]$ $\left[\begin{array}{rr}1 & 1 \\ -1 & -2\end{array}\right]$ $\left[\begin{array}{rr}2 & 1 \\ -1 & -1\end{array}\right]$ $\left[\begin{array}{rr}0 & 1 \\ -2 & -3\end{array}\right]$ Control Systems gate2007-ec control-systems linear-algebra state-equations + – admin 183 views answer comment Share Follow Add Sync Questions Print 0 reply Please log in or register to add a comment.
