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.TH rowinout 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
rowinout - inner-outer factorization
.SH CALLING SEQUENCE
.nf
[Inn,X,Gbar]=rowinout(G)
.fi
.SH PARAMETERS
.TP 6
G
: linear system (\fVsyslin\fR list) \fV[A,B,C,D]\fR
.TP
Inn
: inner factor (\fVsyslin\fR list)
.TP
Gbar
: outer factor (\fVsyslin\fR list)
.TP
X
: row-compressor of \fVG\fR (\fVsyslin\fR list)
.SH DESCRIPTION
Inner-outer factorization (and row compression) of (\fVl\fRx\fVp\fR) \fVG =[A,B,C,D]\fR with \fVl>=p\fR.
.LP
\fVG\fR is assumed to be tall (\fVl>=p\fR) without zero on the imaginary axis
and with a \fVD\fR matrix which is full column rank.
.LP
\fVG\fR must also be stable for having \fVGbar\fR stable.
.LP
\fVG\fR admits the following inner-outer factorization:
.nf
G = [ Inn ] | Gbar |
| 0 |
.fi
where \fVInn\fR is square and inner (all pass and stable) and \fVGbar\fR
square and outer i.e:
Gbar is square bi-proper and bi-stable (Gbar inverse is also proper
and stable);
.LP
Note that:
.nf
[ Gbar ]
X*G = [ - ]
[ 0 ]
.fi
is a row compression of \fVG\fR where \fVX\fR = \fVInn\fR inverse is all-pass i.e:
.nf
T
X (-s) X(s) = Identity
.fi
(for the continous time case).
.SH SEE ALSO
syslin, colinout
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