There is two types of state space models:
The classic one:
$$\dot{x} = Ax + Bu + \omega$$ $$y = Cx + Du + \upsilon $$
Where $A$ is the system matrix, $B$ is the insignal matrix, $C$ is the output matrix, $D$ is the direct matrix, $\omega$ is the disturbance vector and $\upsilon$ is the noise vector. Normaly those vectors often are multiplied with a diagonal matrix.
Then we have the...other state space model:
$$\dot{x} = Ax + Bu + \omega$$ $$ z = Mx + D_z u $$ $$y = Cx + D_y u + \upsilon $$
So...what are $$ z = Mx + D_z u $$
supposed to be? Let me guess! The $z$ variable is only for loop shaping controllers which look like this:
And this: $$y = Cx + D_y u + \upsilon $$
Is only for measurement and this:
$$ z = Mx + D_z u $$
Is only for optimizing showing which state are the state who going to the observable state?
For example:
If $C$ are:
$$ C = \begin{bmatrix} 1 & 0 &0 \\ 0 & 1 & 0\\ 0 & 0 & 1 \end{bmatrix} $$
And we want to measure all states $x$ just by one state. Let's say $x_3$. That means that $M$ are going to be:
$$M = \begin{bmatrix} 0 & 0 & 1 \end{bmatrix}$$
Right? So the classical state space model's $C$ matrix is the new $M$ matrix?
Performance variables, i.e. the variables you actually want to control, in contrast to $y$ which are the measured signals.