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 continous time case).

See also