Continuous-Time Linear Dynamical Systems with Inputs and Outputs
Definition
A continuous-time time-invariant
linear dynamical system is a tuple $(A,
B, C, D)$ where $A \in \R ^{n \times n}$, $B
\in \R ^{n \times m}$, $C \in \R ^{k \times
n}$ and $D \in \R ^{k \times m}$.
Given an input $u: \R
\to \R ^m$, it models a
state $x: \R \to \R ^n$
and output $y: \R \to
\R ^k$ by
\[
\begin{aligned}
\dot{x} &= Ax + Bu, \\
y &= Cx + Du.
\end{aligned}
\]