Consider the electrical network shown in the figure in state space, where iR(t) is the output.
Which of the following represents the state space for the above circuit.
1
\(\dot x = \left[ {\begin{array}{*{20}{c}}
{\frac{{ - 1}}{9}}&{\frac{{ - 1}}{3}}\\
{\frac{{ - 11}}{2}}&{\frac{{ - 3}}{2}}
\end{array}} \right]x + \left[ {\begin{array}{*{20}{c}}
{\frac{1}{9}}\\
0
\end{array}} \right]{V_i},\;\;y = \left[ {4\;\;1} \right]x\)
2
\(\dot x = \left[ {\begin{array}{*{20}{c}}
{\frac{1}{9}}&{\frac{1}{3}}\\
{\frac{{ - 11}}{2}}&{\frac{{ - 3}}{2}}
\end{array}} \right]x + \left[ {\begin{array}{*{20}{c}}
{\frac{1}{9}}\\
0
\end{array}} \right]{V_i},\;\;y = \left[ {4\;\;1} \right]x\)
3
\(\dot x = \left[ {\begin{array}{*{20}{c}}
{\frac{{ - 1}}{9}}&{\frac{{ - 1}}{3}}\\
{\frac{{11}}{2}}&{\frac{3}{2}}
\end{array}} \right]x + \left[ {\begin{array}{*{20}{c}}
{\frac{1}{9}}\\
0
\end{array}} \right]{V_i},\;\;y = \left[ {4\;\;1} \right]x\)
4
\(\dot x = \left[ {\begin{array}{*{20}{c}}
{\frac{1}{9}}&{\frac{1}{3}}\\
{\frac{{11}}{2}}&{\frac{3}{2}}
\end{array}} \right]x + \left[ {\begin{array}{*{20}{c}}
{\frac{1}{9}}\\
0
\end{array}} \right]{V_i},\;\;y = \left[ {4\;\;1} \right]x\)