# rowinout

inner-outer factorization

## Calling Sequence

    [Inn,X,Gbar]=rowinout(G)

## Arguments

G

  linear system (`syslin` list) `[A,B,C,D]`

Inn

  inner factor (`syslin` list)

Gbar

  outer factor (`syslin` list)

X

  row-compressor of `G` (`syslin` list)

## Description

Inner-outer factorization (and row compression) of (`l`x`p`) `G =[A,B,C,D]` with `l>=p`.

`G` is assumed to be tall (`l>=p`) without zero on the imaginary axis and with a `D` matrix which is full column rank.

`G` must also be stable for having `Gbar` stable.

`G` admits the following inner-outer factorization:

     G = [ Inn ] | Gbar |
                 |  0   |

where `Inn` is square and inner (all pass and stable) and `Gbar` square and outer i.e: Gbar is square bi-proper and bi-stable (Gbar inverse is also proper and stable);

Note that:

          [ Gbar ]
    X*G = [  -   ]
          [  0   ]

is a row compression of `G` where `X` = `Inn` inverse is all-pass i.e:

     T
    X (-s) X(s) = Identity

(for the continuous time case).

## See Also

- syslin
- colinout