% Fichier ex4.6.tex - Ch. Rolland/O Reilly France
\documentclass{article}
\usepackage[latin1]{inputenc}
\begin{document}
$$
\left\{
  \begin{array}{l}
    \dot{x}(t)=
    \left(
      \begin{array}{ccccc}
        0                     & 1    & 0      &         & 0       \\
        \vdots                &      & \ddots & \ddots  &         \\
        0                     &      &        & \ddots  & 0       \\
        \underline{\hat{a}}_k &      &        & 0       & 1       \\
        -a_0                  & -a_1 & \ldots & \ldots  & -a_{n-1}\\
      \end{array}
    \right)
    x(t) +
    \left(
      \begin{array}{c}
        0     \\
        \vdots\\
        0     \\
        \vdots\\
        1     \\
      \end{array}
    \right)
    e(t)
    \\
    \\
    s(t)= 
    \left(
      \begin{array}{ccccccc}
         b_0 & b_1 & \ldots & b_m & 0 & \ldots & 0\\
      \end{array}
    \right)
    x(t)
  \end{array}
\right.
$$
avec~: 
$$
\underbrace{
  \underline{\hat{a}}_k=
  \left[
    \sum_{i=1}^k 
    \frac{\underline{x}_i \underline{x}_i^T}
         {\sigma_i^2}
  \right]^{-1}
  \left[
    \sum_{i=1}^k
    \frac{\underline{x}_i y_i}
         {\sigma_i}
  \right]
}_{D'apr\grave{e}s\ la\ r\grave{e}gle\ 
   \acute{e}nonc\acute{e}e\ plus\ haut}
\hspace{1cm} \forall k, tel\ que\ 1\leq k < N
$$
\end{document}
