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dt_ility Scilab Group Scilab Function dt_ility
NAME
dt_ility - detectability test
CALLING SEQUENCE
[k, [n [,U [,Sld ] ] ]]=dt_ility(Sl [,tol])
PARAMETERS
Sl : linear system (syslin list)
n : dimension of unobservable subspace
k : dimension of unstable, unobservable subspace ( k<=n ).
U : orthogonal matrix
Sld : linear system (syslin list)
tol : threshold for controllability test.
DESCRIPTION
Detectability test for sl, a linear system in state-space representation.
U is a basis whose k first columns span the unstable, unobservable
subspace of Sl (intersection of unobservable subspace of (A,C) and
unstable subspace of A). Detectability means k=0.
Sld = (U'*A*U,U'*B,C*U,D) displays the "detectable part" of Sl=(A,B,C,D),
i.e.
[*,*,*]
U'*A*U = [0,*,*]
[0,0,*]
C*U = [0,0,*]
with (A33,C3) observable (dimension nx-n), A22 stable (dimension n-k)
and A11 unstable (dimension k).
EXAMPLE
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")
SEE ALSO
contr, st_ility, unobs, stabil
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