Laplace Transform of a State-Space Model

4 May 15, 2024

With the state-space model defined in the time domain as
$$
\begin{matrix}
\dot{x}(t)=Ax(t)+Bu(t) \\
y(t)=Cx(t)+Du(t)
\end{matrix}$$
The Laplace transform then becomes.
$$
\begin{matrix}
sx(s)-x(0)=Ax(s)+Bu(s)\\
y(s)=Cx(s)+Du(s)
\end{matrix}$$

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[[Laplace Transform]]
[[State-Space Model]]