[Tex/LaTex] State Space representation

Question

I am looking for a nice state space representation. Does someone know how to place text left to the equation in a split environment? What environment should be used for the explanations?

\usepackage{mathtools}

\begin{document}
This looks nice
    \begin{align}
        \begin{split}
            \mathbf{\dot{x}}_z &= \mathbf{A}_z \mathbf{x}_z +\mathbf{B}_z \mathbf{u}_z\\
            \mathbf{y}_z &= \mathbf{C}_z \mathbf{x}_z + \mathbf{D}_z \mathbf{u}_z 
        \end{split}
    \end{align}
A -- Matrix\hspace{15pt}\hspace{15pt}\hspace{15pt}u - Vector 

B -- Matrix\hspace{15pt}\hspace{15pt}\hspace{15pt}z - Vector 

C -- Matrix\hspace{15pt}\hspace{15pt}\hspace{15pt}y - Vector 

D - Matrix\\


Here the spacing of the equation number is improvable
    \begin{align}
        \begin{split}
                \\[\medskipamount]
            \text{some text}\quad
            \mathbf{\dot{x}}_z &= \mathbf{A}_z \mathbf{x}_z +\mathbf{B}_z \mathbf{u}_z
                            \\[\medskipamount]
            \text{another text}\quad
            \mathbf{y}_z &= \mathbf{C}_z \mathbf{x}_z + \mathbf{D}_z \mathbf{u}_z 
        \end{split}
    \end{align}
Here an annother approach\\
some text:\hspace{65pt}$\mathbf{z}=\mathbf{A}_z \mathbf{x}_z +\mathbf{B}_z \mathbf{u}_z$ 

some text:\hspace{65pt}$\mathbf{y}_z = \mathbf{C}_z \mathbf{x}_z + \mathbf{D}_z \mathbf{u}_z $\\ 

A -- Matrix\hspace{15pt}\hspace{15pt}\hspace{15pt}u - Vector 

B -- Matrix\hspace{15pt}\hspace{15pt}\hspace{15pt}z - Vector 

C -- Matrix\hspace{15pt}\hspace{15pt}\hspace{15pt}y - Vector 

D - Matrix


\end{document}

Answer 1

For this purpose, I usually use the flalign of mathtools/amsmathand the \text{ } command of amsmath:

\documentclass{article}
\usepackage{mathtools}
\begin{document}

\begin{flalign}
&\text{Equation 1} &\mathbf{\dot{x}}_z &= \mathbf{A}_z \mathbf{x}_z +\mathbf{B}_z \mathbf{u}_z&\nonumber\\
&\text{Equation 2} &\mathbf{y}_z       &= \mathbf{C}_z \mathbf{x}_z + \mathbf{D}_z \mathbf{u}_z& 
\end{flalign}

\begin{flalign*}
&\text{A -- System Matrix} &u\text{-Vector 1}&&\\
&\text{B -- Input Matrix } &z\text{-Vector 2}&&\\
&\text{C -- Output Matrix} &y\text{-Vector 2}&&\\
&\text{D -- Output Matrix} &                 &&
\end{flalign*}

\end{document}

Please notice the initial and final &.

The centering of the equation number is more tricky but a solution is provided below.

EDIT : this is in fact a duplicate of Use flalign or alignat or align or similar environment to align to the left

EDIT2 : The expected result can be achieved bu using flalign only to get the flushleft effect and the single centered line number; and inserting the annotated equations in an aligned:

\begin{flalign} 
&\begin{aligned}
&\text{Equation 1}    \qquad &\mathbf{\dot{x}}_z &= \mathbf{A}_z \mathbf{x}_z +\mathbf{B}_z \mathbf{u}_z\\
&\text{Equation 222}  \qquad &\mathbf{y}_z       &= \mathbf{C}_z \mathbf{x}_z + \mathbf{D}_z \mathbf{u}_z
\end{aligned}&
\end{flalign}