New answers tagged state-space
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First Order State Space Question
In this system, the state (𝑥(𝑡)) and "output" (𝑦(𝑡)) are the same (both scalars)
They don't have to be.
Why do we instead get 𝐶=1𝜏 and a separation between the state and output?
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Accepted
First Order State Space Question
If $X(s)$ and $Y(s)$ are the input and output in the Laplace domain, respectively, we have
$$Y(s)(s\tau +1)=X(s)\tag{1}$$
In the time domain, this is equivalent to
$$\tau y'(t)+y(t)=x(t)\tag{2}$$
It ...
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2
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Accepted
Does every continuous-time filter have a state-space representation?
Well, yes and no. Yes, but you may not be able to recognize it in the end -- or find an agreed-upon and useful representation for it.
If the system (a filter is just a system, so I'm going to use the ...
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Does every continuous-time filter have a state-space representation?
The answer is "yes" but not a unique state space representation.
There is a unique representation that guarantees observability and a unique representation that guarantees controllability. ...
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