Parameters

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