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Discrete-Time Linear State Space Models

For linear, time-invariant systems, a discrete-time state-space model looks like a vector first-order finite-difference model:

\begin{eqnarray*}
\underline{x}(n+1) & = & \mathbf{A}\, \underline{x}(n) + \mathbf{B}\, \underline{u}(n) \nonumber \\
\underline{y}(n) & = & \mathbf{C}\, \underline{x}(n) + \mathbf{D}\,\underline{u}(n)
\end{eqnarray*}

where

The state-space representation is especially powerful for


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Download StateSpace.pdf
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``Introduction to State Space Models'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2015-04-18 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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