GATE EC 2017 Set 2 Q47 — Control Systems

A second-order LTI system is described by the following state equations, $$\begin{array}{ll} \frac{d}{dt}x_1(t)-x_2(t)=0 \\ \frac{d}{dt}x_2(t)+2x_1(t)+3x_2(t)=r(t) \end{array}$$

where $x_1(t)$ and $x_2(t)$ are the two state variables and $r(t)$ denotes the input. The output $c(t)=x_1(t)$. The system is