# stabsep

Stable-unstable decomposition

## Syntax

## Description

`[`

decomposes the linear time-invariant (LTI) model `G1`

,`G2`

] = stabsep(`G`

)`G`

into its stable and
unstable parts.

$$G={G}_{1}+{G}_{2}$$

`G1`

contains all stable modes (poles) that can be separated from the
unstable modes in a numerically stable way, and `G2`

contains the
remaining modes. `G1`

is always proper and contains the feedthrough term
(if any).

`[`

specifies additional options for controlling accuracy or focusing on unstable modes.`G1`

,`G2`

] = stabsep(`G`

,___,`Name=Value`

)* (since R2023b)*

## Examples

## Input Arguments

## Output Arguments

## References

[1] Bartels, R. H., and G. W. Stewart.
“Algorithm 432 [C2]: Solution of the Matrix Equation AX + XB = C [F4].”
*Communications of the ACM* 15, no. 9 (September 1972): 820–26.
https://doi.org/10.1145/361573.361582.

[2] Bavely, Connice A., and G. W.
Stewart. “An Algorithm for Computing Reducing Subspaces by Block Diagonalization.”
*SIAM Journal on Numerical Analysis* 16, no. 2 (April 1979): 359–67.
https://doi.org/10.1137/0716028.

[3] Demmel, James. “The Condition
Number of Equivalence Transformations That Block Diagonalize Matrix Pencils.” *SIAM
Journal on Numerical Analysis 20*, no. 3 (June 1983): 599–610.
https://doi.org/10.1137/0720040.

## Version History

**Introduced before R2006a**