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I want to ask about this scheme: enter image description here

$u_0$ should be something as input in specific point given by the initial conditions and $y_0$ output. Block State Spase represented linearized system by A, B, C, D state metrices.

And I'm wondering why there is "-" by $u_0$ and "+" by $y_0$. Is this scheme universal? Why does it look like it looks?

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The scheme is not universal.

One reason to do it is to allow the system to be modeled around a set-point or bias level ($u_0$) without having that set-point affect the state space model.

Subtracting the set-point, doing the state space equations, and then adding back on the corrected set-point ($y_0$) lets you do this.

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