Problem 2: A (battery) system has the state equation
$\dot{x} = \begin{bmatrix} 0 & 0 \\ 0 & -\frac{1}{R_p C_p} \end{bmatrix} x + \begin{bmatrix} \frac{1}{Q} \\ \frac{1}{C_p} \end{bmatrix} i$
v = [c, 1]x
where Q = 36000, $C_p$ = 500, $R_p$ = 0.2, c = 0.5.
(1) Check if the system is observable.
(2) Design a state observer to estimate x (we need to estimate the SOC),
such that the observation error dynamic system has poles at -1, -2.