# getrom

## Description

Use `getrom`

to obtain reduced-order models from a
`BalancedTruncation`

or `SparseBalancedTruncation`

model
order reduction task. For the full workflow, see Task-Based Model Order Reduction Workflow.

returns a reduced-order model `rsys`

= getrom(`R`

,`Name=Value`

)`rsys`

based on the options specified by
one or more name-value arguments.

returns a simplified model `rsys`

= getrom(`R`

)`rsys`

.

For ordinary balanced truncation,

`rsys`

is a simplified model where all states associated with numerically zero Hankel singular values (HSVs) are removed. This amounts to a minimal realization of the original system`sys`

For sparse balanced truncation,

`rsys`

is the reduced-order model associated with the computed HSVs. These are the (numerically nonzero) singular values of*L*, where_{r}^{T}L_{o}*L*and_{r}*L*are the low-rank Gramian factors available in_{o}`R`

. Since*L*and_{r}*L*are tall and skinny, the order of_{o}`rsys`

is typically much smaller than the order of`sys`

. You can further reduce the order by dropping states with relatively small HSVs.

`getrom(`

returns help specific to
the model order specification object `R`

,"-help")`R`

. The returned help shows the
name-value arguments and syntaxes applicable to `R`

.

## Examples

## Input Arguments

## Output Arguments

## More About

## References

[1] Benner, Peter, Jing-Rebecca Li,
and Thilo Penzl. “Numerical Solution of Large-Scale Lyapunov Equations, Riccati Equations, and
Linear-Quadratic Optimal Control Problems.” *Numerical Linear Algebra
with Applications* 15, no. 9 (November 2008): 755–77.
https://doi.org/10.1002/nla.622.

[2] Benner, Peter, Martin Köhler, and
Jens Saak. “Matrix Equations, Sparse Solvers: M-M.E.S.S.-2.0.1—Philosophy, Features, and
Application for (Parametric) Model Order Reduction.” In *Model
Reduction of Complex Dynamical Systems*, edited by Peter Benner, Tobias Breiten,
Heike Faßbender, Michael Hinze, Tatjana Stykel, and Ralf Zimmermann, 171:369–92. Cham:
Springer International Publishing, 2021.
https://doi.org/10.1007/978-3-030-72983-7_18.

[3] Varga, A. “Balancing Free
Square-Root Algorithm for Computing Singular Perturbation Approximations.” In *[1991] Proceedings of the 30th IEEE Conference on Decision and
Control*, 1062–65. Brighton, UK: IEEE, 1991.
https://doi.org/10.1109/CDC.1991.261486.

[4] Green, M. “A Relative Error Bound
for Balanced Stochastic Truncation.” *IEEE Transactions on Automatic
Control* 33, no. 10 (October 1988): 961–65.
https://doi.org/10.1109/9.7255.

## Version History

**Introduced in R2023b**