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.TH dt_ility 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
dt_ility - detectability test
.SH CALLING SEQUENCE
.nf
[k, [n [,U [,Sld ] ] ]]=dt_ility(Sl [,tol])
.fi
.SH PARAMETERS
.TP 10
Sl
: linear system (\fVsyslin\fR list)
.TP 10
n
: dimension of unobservable subspace
.TP
k
: dimension of unstable, unobservable subspace (\fV k<=n \fR).
.TP
U
: orthogonal matrix
.TP
Sld
: linear system (\fVsyslin\fR list)
.TP
tol
: threshold for controllability test.
.SH DESCRIPTION
Detectability test for \fVsl\fR, a linear system in state-space
representation.
\fVU\fR is a basis whose \fVk\fR first columns span the
unstable, unobservable subspace of \fVSl\fR (intersection
of unobservable subspace of \fV(A,C)\fR and unstable subspace
of \fVA\fR). Detectability means \fVk=0\fR.
.LP
\fVSld = (U'*A*U,U'*B,C*U,D)\fR displays the "detectable part"
of \fVSl=(A,B,C,D)\fR, i.e.
.nf
[*,*,*]
U'*A*U = [0,*,*]
[0,0,*]
C*U = [0,0,*]
.fi
with \fV(A33,C3)\fR observable (dimension \fVnx-n\fR), \fVA22\fR stable
(dimension \fVn-k\fR) and \fVA11\fR unstable (dimension \fVk\fR).
.SH EXAMPLE
.nf
A=[2,1,1;0,-2,1;0,0,3];
C=[0,0,1];
X=rand(3,3);A=inv(X)*A*X;C=C*X;
W=syslin('c',A,[],C);
[k,n,U,W1]=dt_ility(W);
W1("A")
W1("C")
.fi
.SH SEE ALSO
contr, st_ility, unobs, stabil
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