[Tex/LaTex] Align multiple equations inside tabular with case environment.

aligntables

I want to align the equations inside a tabular environment, those equations contain a case environment such that the alignment becomes annoying, the following figure shows what trouble I encountered, how could I solve this problem?

enter image description here

The Latex codes are 

\documentclass[preview]{standalone}
\usepackage{amsmath}
\usepackage[flushleft]{threeparttable}
\usepackage{makecell,booktabs}
\begin{document}
\newsavebox\CE 
\begin{lrbox}{\CE}
$\begin{aligned}
\hat{x}^i_k & = \hat{x}^i_{k\mid {k-1}}+ K^i_k( z^{i}_k - H^i_k \hat{x}^i_{k \mid k-1})+u^i_k  \notag\\
u^i_k&=C^i_k \sum_{j\in N_i}(\hat{x}^j_{{k-1}}-\hat{x}^i_{k\mid {k-1}} ) 
\end{aligned}
$
\end{lrbox}


\newsavebox\HC
\begin{lrbox}{\HC}
$\begin{aligned}
\begin{cases}
\hat{x}^i_k & = A_k \hat{x}^i_{ {k-1}}+ K^i_k( z^{i}_k - H^i_k \hat{x}^i_{ k-1})+u^i_k  \notag\\
u^i_k&=C^i_k \sum_{j\in N_i}(\hat{x}^j_{{k-1}}-\hat{x}^i_{ {k-1}} )
\end{cases}\\ 
& Subject To\\
\frac{1}{n}\sum_{i\in \mathcal{N}} \|\tilde{z}^i\|^2 &\leq \gamma^2 \{ \|v\|_2^2 +\frac{1}{n}\sum_{i\in \mathcal{N}} (e^i_0)^T S^i e^i_0\}
\end{aligned}
$
\end{lrbox}
\begin{table}
  \caption{The mechanisms of four consensus filtering approaches}
  \centering
  \begin{threeparttable}
    \begin{tabular}{cc@{\qquad}}
    Types  & Structures of Consensus Filters\\
       \midrule\midrule 
        \makecell{CE} & \usebox{\CE}  \\\cmidrule(l r){1-2}
      \makecell{$H_\infty$\\ consensus} & \usebox{\HC}  \\ \midrule\midrule
    \end{tabular}
       \end{threeparttable}
  \end{table}
\end{document}

Best Answer

I only guess how you like to your table look out: Something like this:

enter image description here

For above image I rewrote (simplify) your MWE:

\documentclass[border=3mm,preview]{standalone}
\usepackage{amsmath}
%\usepackage[flushleft]{threeparttable}
\usepackage{array,booktabs}
\usepackage[font=small]{caption}

    \begin{document}

\begin{table}
  \caption{The mechanisms of four consensus filtering approaches}
  \centering
    \begin{tabular}{m{22mm} m{66mm}}
    Types  & Structures of Consensus Filters\\
     \midrule\midrule
CE  &   
$\begin{aligned}
\hat{x}^i_k & = \hat{x}^i_{k\mid k-1} + K^i_k(z^i_k 
                - H^i_k \hat{x}^i_{k \mid k-1})+u^i_k   \\
      u^i_k & = C^i_k \sum_{j\in N_i}(\hat{x}^j_{k-1}-\hat{x}^i_{k\mid k-1})
\end{aligned}
$                                   \\%new row
    \cmidrule(l r){1-2}
$H_\infty$\newline 
consensus 
    &   $\begin{aligned}
    &   \begin{cases}
\hat{x}^i_k = A_k \hat{x}^i_{k-1} 
                    + K^i_k(z^i_k- H^i_k\hat{x}^i_{k-1})
                    + u^i_k     \\
      u^i_k = C^i_k \sum_{j\in N_i}(\hat{x}^j_{k-1}-\hat{x}^i_{k-1})
        \end{cases}\\
    & \text{Subject To:}\\
    & \frac{1}{n}\sum_{i\in \mathcal{N}} \|\tilde{z}^i\|^2 
            \leq \gamma^2 \{\|v\|_2^2 
              + \frac{1}{n}\sum_{i\in\mathcal{N}} (e^i_0)^T S^i e^i_0\}
\end{aligned}
$                               \\% end of rows
    \midrule\midrule
    \end{tabular}
  \end{table}
\end{document}

As you can see, I wrote equations directly into table. In them I omit all needlessness and also wrote "subject to" as text. I preserve left align of equations.

Instead column type c I use m{>width>} (here you can select width on your taste). This column type make vertical centered and left aligned content of cells. If you like to have horizontally centered to, than instead m{<width>} use:

>{\centering\arraybackslash}m{<width>}

I do not know, what is purpose of use threeparttable, anyway I omit it since it hasn't influence of table appearance with exception of caption. For it I rather use caption package.

Edit: Even better look out you obtain if you erase ampersand in cases environment, as suggested @egreg in his comment.

Related Question