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Differential Equations
Real Matrices
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Continuous-Time Linear Dynamical Systems with Inputs and Outputs
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Autonomous Continuous-Time Linear Dynamical Systems


An autonomous continuous-time linear dynamical system is a matrix $A \in \R ^{n \times n}$. It models the behavior of a signal $x: \R \to \R ^n$ by

\begin{equation} \dot{x} = Ax, \label{defining} \end{equation}
where $\dot{x}$ is notation for $\frac{d}{dt} x(t)$. $A$ is called the dynamics matrix.

A signal $x$ satisfying Equation~\eqref{defining} is called a solution or a trajectory. For $t \in \R $, $x(t) \in \R ^n$ is called the state and $\R ^n$ is called the state space. $n$ is called the state dimension.

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