Chemical Reactor Model

The following two-dimensional single-input single-output system represents a chemical reactor model

$$\begin{align*} \dot{x}_1 &= u(Ce -x_1) - rx_1 \\ \dot{x}_2 &= rx_1 - ux_2 \\ y &= x_1 - x_2, \end{align*}$$

where coefficients are in $\mathbb{R}$, $x_1$ and $x_2$ denote the reactant and product concentrations, respectively. The input $u$ corresponds to the input flow of reactant, $r$ and $C_e$ denote kinetic and reactor parameters.