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The second order dynamic system

$\frac{dX}{dt}=PX+Qu$

$y=RX$

has the matrices $P$, $Q$ and $R$ as follows:

$P=\begin{bmatrix} -1 & 1\\ 0& -3 \end{bmatrix}$ $Q=\begin{bmatrix} 0\\1 \end{bmatrix}$ $R=\begin{bmatrix} 0 & 1 \end{bmatrix}$

The system has the following controllability and observability properties:

- Controllable and observable
- Not controllable but observable
- Controllable but not observable
- Not controllable and not observable

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