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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)]
$

The general case of output extraction is shown in Fig.1.5.

Figure: Continuous-time state-space model with output vector $ \underline{y}(t) = o_t[\underline{x}(t),\underline{u}(t)]$ .
\includegraphics{eps/statespaceanalogwo}

The output signal (vector) is most typically a linear combination of state variables and possibly the current input:

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

where $ C$ and $ D$ are constant matrices of linear-combination coefficients.


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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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