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$$x_1=A\sin{\omega t}$$ $$x_2=\dot{x}_1=A\omega \cos{\omega t}$$ $$y=A\omega$$

We want to represent this system in a state space model. The state transition matrix read:

$$A=\begin{bmatrix} 0 & 1 &\\ -\omega^2 & 0 \\ \end{bmatrix}$$ I am not sure what the output matrix will be like. Can we say

$$y=A\omega=\frac{-x_2}{\cos{\omega t}}$$

So that:

$$C=\begin{bmatrix} 0 & \frac{-1}{\cos{\omega t}} \end{bmatrix}$$

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# State Space: time dependent states but time-independent output

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