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Forming Outputs

Any system output is some function of the state, and possibly the input (directly):

$\displaystyle \underline{y}(t) \isdef o_t[\underline{x}(t),\underline{u}(t)]
$

\begin{center}
\epsfig{file=eps/statespaceanalogwo.eps,width=5in} \\
\end{center}


Usually the output is a linear combination of state variables and possibly the current input:

$\displaystyle \underline{y}(t) \isdefs \mathbf{C}\underline{x}(t) + \mathbf{D}\underline{u}(t)
$

where $ \mathbf{C}$ and $ \mathbf{D}$ are constant matrices of linear-combination coefficients


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Download StateSpace.pdf
Download StateSpace_2up.pdf
Download StateSpace_4up.pdf

``Introduction to State Space Models'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2019-02-05 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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