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dt_ility
detectability test
Syntax
[k, n, U, Sld] = dt_ility(Sl) [k, n, U, Sld] = dt_ility(Sl, tol)
Arguments
- 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
).
Examples
See also
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