# rowinout

inner-outer factorization

### Syntax

[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: `X`

(for the continuous time case).^{t}(-s).X(s) = Identity

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