Balanced Truncation

Available identifiers

MaRDI QIDQ6684550

powerful technique to reduce the state-space dimension of a dynamical system

Description

The basic principle is to identify a subspace of jointly easily controllable and observable states and then to restrict the dynamics to this subspace, hopefully without changing the overall response of the system too much.

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List of mathematical expressions with quantities

Balancing Transformation	$T^{-1}{W}_c{\left(T^{-1}\right)}^{*}=T^{*}{W}_{o}T=\left(\begin{array}{lll}{\sigma }_1& & 0\\ & \ddots & \\ 0& & {\sigma }_n\end{array}\right)=\mathrm{\Sigma }$
$T$ symbol represents MOR Transformation Matrix
$W_c$ symbol represents Gramian Matrix Controllability
$W_o$ symbol represents Gramian Matrix Observability
$\sigma$ symbol represents Hankel Singular Value
Lyapunov Equation	$AX+X{A}^H+Q=0$
$X$ symbol represents Unknown Matrix

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Computational tasks specializing Balanced Truncation

Balanced Truncation (Linear)

Balanced Truncation (Bi-linear)

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