rowinout

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 (lxp) 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