macros.tex

由matlab开发的hybrid系统的描述语言

%% packages
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\usepackage{verbatim}
\usepackage{cite}
\usepackage{graphicx}
\usepackage{amssymb}   %Serve per definire $\rr$, $\Z$, $\N$
\usepackage{latexsym}  %Serve per $\Box$ in \cvd
\usepackage{amsmath}   %Serve per subequation
\usepackage{amsfonts}
\usepackage{rotating}
\usepackage{subfigure}
\usepackage{url}
\usepackage{psfrag}
\usepackage{theorem}
\usepackage{array}


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}
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\newtheorem{lemma}{Lemma}
\newtheorem{fact}{Fact}
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{\theorembodyfont{\rmfamily\small}
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\newcommand{\MLDsystem}[2]{
\begin{subequations}
    \label{#1}
\begin{eqnarray}
    \label{#1.a}
    \left[\begin{smallmatrix}
      x_{r}(t+1)\\
      x_{b}(t+1) \
    \end{smallmatrix}\right]&=&\left[\begin{smallmatrix}
      A_{rr} & A_{rb} \\
      A_{br} & A_{bb} \
    \end{smallmatrix}\right]    \left[\begin{smallmatrix}
      x_{r}(t)\\
      x_{b}(t) \
    \end{smallmatrix}\right]+\left[\begin{smallmatrix}
      B_{1rr} & B_{1rb} \\
      B_{1br} & B_{1bb} \
    \end{smallmatrix}\right]    \left[\begin{smallmatrix}
      u_{r}(t)\\
      u_{b}(t) \
    \end{smallmatrix}\right]\\\nonumber
    &&+\left[\begin{smallmatrix}
      B_{2rb} \\
      B_{2bb} \
    \end{smallmatrix}\right]d(t)+\left[\begin{smallmatrix}
      B_{3rr} \\
      B_{3br} \
    \end{smallmatrix}\right]z(t),     \\
    \label{#1.b}
        \left[\begin{smallmatrix}
      y_{r}(t)\\
      y_{b}(t) \
    \end{smallmatrix}\right]&=&\left[\begin{smallmatrix}
      C_{rr} & C_{rb} \\
      C_{br} & C_{bb} \
    \end{smallmatrix}\right]    \left[\begin{smallmatrix}
      x_{r}(t)\\
      x_{b}(t) \
    \end{smallmatrix}\right]+\left[\begin{smallmatrix}
      D_{1rr} & D_{1rb} \\
      D_{1br} & D_{1bb} \
    \end{smallmatrix}\right]    \left[\begin{smallmatrix}
      u_{r}(t)\\
      u_{b}(t) \
    \end{smallmatrix}\right]\\\nonumber
    &&+\left[\begin{smallmatrix}
      D_{2rb} \\
      D_{2bb} \
    \end{smallmatrix}\right]d(t)+\left[\begin{smallmatrix}
      D_{3rr} \\
      D_{3br} \
    \end{smallmatrix}\right]z(t),     \\
    \label{#1.c}
    E_{2}d(t)&+&E_{3}z(t)\leq
E_{1} \left[\begin{smallmatrix}
      u_{r}(t)\\
      u_{b}(t) \
    \end{smallmatrix}\right] +
E_{2} \left[\begin{smallmatrix}
      x_{r}(t)\\
      x_{b}(t) \
    \end{smallmatrix}\right]
    +E_{5}{\rm #2}
\end{eqnarray}
\end{subequations}
}

\newcommand{\BDMLDsystem}[2]{
\begin{subequations}
    \label{#1}
\begin{eqnarray}
    \label{#1.a}
    \left[\begin{smallmatrix}
      x_{r}(t+1)\\
      x_{b}(t+1) \
    \end{smallmatrix}\right]&=&\left[\begin{smallmatrix}
      A_{rr} & A_{rb} \\
      A_{br} & A_{bb} \
    \end{smallmatrix}\right]    \left[\begin{smallmatrix}
      x_{r}(t)\\
      x_{b}(t) \
    \end{smallmatrix}\right]+\left[\begin{smallmatrix}
      B_{1rr} & B_{1rb} \\
      B_{1br} & B_{1bb} \
    \end{smallmatrix}\right]    \left[\begin{smallmatrix}
      u_{r}(t)\\
      u_{b}(t) \
    \end{smallmatrix}\right]\\\nonumber
    &&+\left[\begin{smallmatrix}
      B_{2rb} \\
      B_{2bb} \
    \end{smallmatrix}\right]d(t)+\left[\begin{smallmatrix}
      B_{3rr} \\
      B_{3br} \
    \end{smallmatrix}\right]z(t) + \left[\begin{smallmatrix}
    B_{5r} \\
    B_{5b} \
    \end{smallmatrix}\right], \\
    \label{#1.b}
        \left[\begin{smallmatrix}
      y_{r}(t)\\
      y_{b}(t) \
    \end{smallmatrix}\right]&=&\left[\begin{smallmatrix}
      C_{rr} & C_{rb} \\
      C_{br} & C_{bb} \
    \end{smallmatrix}\right]    \left[\begin{smallmatrix}
      x_{r}(t)\\
      x_{b}(t) \
    \end{smallmatrix}\right]+\left[\begin{smallmatrix}
      D_{1rr} & D_{1rb} \\
      D_{1br} & D_{1bb} \
    \end{smallmatrix}\right]    \left[\begin{smallmatrix}
      u_{r}(t)\\
      u_{b}(t) \
    \end{smallmatrix}\right]\\ \nonumber
    &&+\left[\begin{smallmatrix}
      D_{2rb} \\
      D_{2bb} \
    \end{smallmatrix}\right]d(t)+\left[\begin{smallmatrix}
      D_{3rr} \\
      D_{3br} \
    \end{smallmatrix}\right]z(t) + \left[\begin{smallmatrix}
    D_{5r} \\
    D_{5b} \
    \end{smallmatrix}\right], \\
    \label{#1.c}
    E_{2}d(t)&+&E_{3}z(t)\leq
E_{1} \left[\begin{smallmatrix}
      u_{r}(t)\\
      u_{b}(t) \
    \end{smallmatrix}\right] +
E_{2} \left[\begin{smallmatrix}
      x_{r}(t)\\
      x_{b}(t) \
    \end{smallmatrix}\right]
    +E_{5}{\rm #2}
\end{eqnarray}
\end{subequations}
}

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