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\begin{document}
\begin{equation*}
  \aligned 
    x_k &= A^k x_0 + \sum_{i=0}^{k-1} A^{k-i-1} B u_i \\
    y_k &= C A^k x_0 + \sum_{i=0}^{k-1} C A^{k-i-1} B u_i + D u_k \\
  \endaligned \qquad k > 0.
\end{equation*}
\end{document}