The static gain state-space model is a reduction of the general form of the state-space model where there are no internal states. There are no internal states that affect each other, so the A matrix is zero. There are no internal states for the inputs to affect; therefore B is also zero. Without states to affect the output, C is zero as well. Therefore the only matrix that has any values is the D matrix or the feedthrough matrix.
$$D=\begin{bmatrix}
1 & 2 \\ 3 & 4
\end{bmatrix}$$
A static gain is the simplest form of a feedback controller.
[[Gain Block Diagram]]
[[Unity-Gain Feedback Example]] – how a unity gain affects a closed-loop system.
[[Static Gain Closed Loop Motor Controller]]
- StatespaceModelMATLAB
- christopherlumBandwidthDynamicSystem2019