I would like to illustrate the structure of two matrices, but unfortunately they become hard to read very quickly. This is because its entries' expressions grow with every line.

The equation looks as follows:

![Matrix structure](https://i.stack.imgur.com/Do2ob.png)

An MWE is:

```
\documentclass{article}

\usepackage{mathtools}

\begin{document}
\begin{multline}
    \underbracket[0pt][0pt]{%
    \begin{pmatrix}
        \mathbf{x}(0) \\
        \mathbf{x}(1) \\
        \mathbf{x}(2) \\
        \vdots \\
        \mathbf{x}(N) 
    \end{pmatrix}
}_{\mathbf{X}}
    = 
    \underbracket[0pt][0pt]{%
    \begin{bmatrix} 
        \eyezero  &     &        &         &  \\
                  & A_0 &        &         &  \\
                  &     & A_1A_0 &         &  \\
                  &     &        & \ddots  &  \\
                  &     &        &         & A_{N-1}A_{N-2}\cdots A_0
    \end{bmatrix} 
}_{S_x}
\underbracket[0pt][0pt]{%
    \begin{pmatrix} 
        \mathbf{x}_0 \\
        \mathbf{x}_0 \\
        \mathbf{x}_0 \\
        \vdots \\
        \mathbf{x}_0 
    \end{pmatrix}
}_{\mathbf{X}_0} \cdots \\*
\hspace*{6em}
    \cdots+ 
    \underbracket[0pt][0pt]{%
        \begin{bmatrix*}[r]
        \zermzero                         &             &        &        & \\
        B_0                               &             &        &        & \\
        A_1 B_0                           & B_{1}       &        &        & \\
        A_2 A_1 B_0                       & A_{2} B_{1} & B_{3}  &        & \\
        \vdots                            & \vdots      & \vdots & \ddots & \\
        A_{N-1}A_{N-2} \cdots A_{1} B_{0} & \cdots      & \cdots & \cdots & B_{N-1} \\
    \end{bmatrix*} 
}_{S_u}
\underbracket[0pt][0pt]{%
    \begin{pmatrix}
        \mathbf{u}(0) \\
        \mathbf{u}(1) \\
        \mathbf{u}(2) \\
        \vdots \\
        \mathbf{u}(N-1)
    \end{pmatrix} 
}_{\mathbf{U}}
\end{multline}

\end{document}

```

Do you have any idea how I can improve the readability of this equation with the tools available in LaTeX?