deletions | additions       diff --git a/counter.tex b/counter.tex  index ceea6dc..3864054 100644  --- a/counter.tex  +++ b/counter.tex 
...
\end{equation}  Hence, $u(k) = \mathcal K(z) y(k) = F \tilde u(k)$. The factorization on $\mK(z)$ implies the CPS diagram illustrated in Fig~\ref{fig:factorization}.  \begin{figure}[ht]  \begin{center}  \begin{tikzpicture}[>=stealth',  box/.style={rectangle, draw=blue!50,fill=blue!20,rounded corners, semithick,minimum size=7mm},  point/.style={coordinate},  every node/.append style={font=\small}  ]  \matrix[row sep = 5mm, column sep = 5mm]{  %first row  \node (p1) [] {$w(k)$};  & \node (noisetransfer) [box] {$\mathcal H(z)$};  &   &\node (p2) [point] {};  &\\  %second row  \node (p3) [point] {};  &\node (plant) [box] {$\mathcal G(z)$};  &   & \node (plus) [circle,draw,inner sep=2pt] {};  & \node (p5) [point] {};\\  %third row  &  &   & \node (p6) [] {$v(k)$};  & \\  %fourth row  \node (p7) [point] {};  &\node (F) [box] {$F$};  &  & \node (controller) [box] {$\tilde \mK (z)$};  & \node (p8) [point] {};\\  };  \draw [semithick,->] (p1)--(noisetransfer);  \draw [semithick,->] (noisetransfer)--(p2)--(plus);  \draw [semithick,->] (p6)--(plus);  \draw [semithick,->] (plant)--(plus);  \draw [semithick,->] (plus)--(p5)-- node[midway,right]{$y(k)$} (p8) -- (controller);  \draw [semithick,->] (controller)-- node[midway,above]{$\tilde u(k)$} (F);  \draw [semithick,->] (F)--(p7)-- node[midway,left]{$u(k)$}(p3)--(plant);  \draw [semithick] (plus.north)--(plus.south);  \draw [semithick] (plus.east)--(plus.west);  \end{tikzpicture}  \end{center}  \caption{The diagram of the CPS with a low-rank controller design, where $\mK(z)$ is factorized into $F\tilde \mK(z)$.}  \label{fig:factorization}  \end{figure}  Since we are restricting ourselves to use a low-rank controller, the performance of the system may not be optimal. In this section, we consider the problem of optimizing the following infinite horizon LQG performance:  \begin{equation}  J = \limsup_{T\rightarrow \infty}\frac{1}{T}\min_{u(k)}\mathbb{E}\left[\sum_{k=0}^{T-1} x(k)^TWx(k)+u(k)^TUu(k)\right],