inner-outer factorization
[Inn,X,Gbar]=rowinout(G)
: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) :
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).