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State Space Models

Equations of motion for any physical system may be conveniently formulated in terms of its state $ \underline{x}(t)$ :

\epsfig{file=eps/statespaceanalog.eps,width=5in}

$\displaystyle \underline{{\dot x}}(t) = f_t[\underline{x}(t),\underline{u}(t)]
$

where

\begin{eqnarray*}
\underline{x}(t) &=& \mbox{\emph{state} of the system at time $t$}\\
\underline{u}(t) &=& \mbox{vector of \emph{external inputs} (typically driving forces)}\\
f_t &=& \mbox{general function mapping the current state $\underline{x}(t)$\ and}\\
&& \mbox{inputs $\underline{u}(t)$\ to the state time-derivative $\underline{{\dot x}}(t)$}
\end{eqnarray*}



Subsections
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``Introduction to State Space Models'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2014-03-24 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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