Forming Outputs

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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

and

are constant matrices of linear-combination coefficients.

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.

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