New answers tagged

0 votes

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? ...
  • 10.1k
0 votes
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 ...
  • 82.3k
2 votes
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 ...
  • 10.1k
1 vote

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. ...

Top 50 recent answers are included