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Aide Scilab >> CACSD > rowinout

# 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 — définition d'un système dynamique linéaire
• colinout — inner-outer factorization

### Comments

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