For the circuit shown in the figure is choose state variables $\mathrm{X}_{1}, \mathrm{X}_{2}, \mathrm{X}_{3^{\prime}}$, to be $i_{\mathrm{L} 1}(t), \mathrm{V}_{c2}(t), i_{\mathrm{L} 3}(t)$
- Write the state equations
\[
\left[\begin{array}{l}
\dot{X}_{1} \\
\dot{X}_{2} \\
\dot{X}_{3}
\end{array}\right]=A\left[\begin{array}{l}
X_{1} \\
X_{2} \\
X_{3}
\end{array}\right]+B[e(t)]
\]
- If $e(t)=0, t \geq 0, i_{L 1}(0)=0, V_{C 2}(0)=0, i_{l 3}(0)=$ $1 \mathrm{~A}$, then what would the total energy dissipated in the resistors in the interval $(0, \infty)$ be ?