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\begin{document}
\begin{equation*}
  \aligned 
    \frac{dx}{dt} &= \begin{bmatrix} -k_0 -k_1 & k_1 - b_0 k \\ k_2 & - k_2 \end{bmatrix} x +
      \begin{bmatrix} b_0 \\ 0 \end{bmatrix} {\mathbf{(u_d + k y_d)}} =: Ax + B {\mathbf{u_e}}, \\
    y &= \begin{bmatrix} 0 & 1 \end{bmatrix} x  =: C x.
  \endaligned
\end{equation*}
\end{document}