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discretization of continuous systems
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Consider a continuous-time system with the following state space representation
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where $x(t)\in\R^n$ , $u(t)\in\R^r$ and $y(t)\in\R^m$ are the state vector, input vector and output vector of the system, respectively; $A\in\R^{n\times n}$ , $B\in\R^{n\times r}$ , $C\in\R^{m\times n}$ and $D\in\R^{m\times r}$ are the constant real or complex matrices.
Suppose that the sampling interval is $\tau$ . By using the step invariance transform or the zero-order hold (ZOH), i.e., $u(t)=u(k\tau),\ k\tau\leq t<(k+1)\tau$ , discretizing the system in (![[*]](http://images.planetmath.org:8080/cache/objects/7827/js//usr/share/latex2html/icons/crossref.png "[*]") ) gives a discrete-time model,
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where $x(k\tau)=x(t)\left|_{t=k\tau}\right.$ , $y(k\tau)=y(t)\left|_{t=k\tau}\right.$ , and \begin{equation}\label{re_01d} G_\tau:=\rme^{A \tau}, \ F_\tau:=\int^{\tau}_{0}\rme^{A t}\rmd t\ B. \end{equation}
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"discretization of continuous systems" is owned by mathcam. [ full author list (2) | owner history (1) ]
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Cross-references: interval, matrices, complex, real, vector, representation, state space
There are 89 references to this entry.
This is version 4 of discretization of continuous systems, born on 2006-04-13, modified 2006-10-04.
Object id is 7827, canonical name is DiscretizationOfContinuousSystems.
Accessed 7084 times total.
Classification:
| AMS MSC: | 93C55 (Systems theory; control :: Control systems, guided systems :: Discrete-time systems) |
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Pending Errata and Addenda
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