Consider a system $S$ represented in state space as
\[
\frac{d x}{d t}=\left[\begin{array}{ll}
0 & -2 \\
1 & -3
\end{array}\right] x+\left[\begin{array}{l}
1 \\
0
\end{array}\right] r, y=\left[\begin{array}{ll}
2 & -5
\end{array}\right] x .
\]
Which of the state space representations given below has/have the same transfer function as that of $S$?
- $\frac{d x}{d t}=\left[\begin{array}{cc}0 & 1 \\ -2 & -3\end{array}\right] x+\left[\begin{array}{l}0 \\ 1\end{array}\right] r, y=\left[\begin{array}{ll}1 & 2\end{array}\right] x$
- $\frac{d x}{d t}=\left[\begin{array}{cc}0 & 1 \\ -2 & -3\end{array}\right] x+\left[\begin{array}{l}1 \\ 0\end{array}\right] r, y=\left[\begin{array}{ll}0 & 2\end{array}\right] x$
- $\frac{d x}{d t}=\left[\begin{array}{cc}-1 & 0 \\ 0 & -2\end{array}\right] x+\left[\begin{array}{l}-1 \\ 3\end{array}\right] r, y=\left[\begin{array}{ll}1 & 1\end{array}\right] x$
- $\frac{d x}{d t}=\left[\begin{array}{cc}-1 & 0 \\ 0 & -2\end{array}\right] x+\left[\begin{array}{l}1 \\ 1\end{array}\right] r, y=\left[\begin{array}{ll}1 & 2\end{array}\right] x$