dt_ility(1)

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).

SEE ALSO
contr, st_ility, unobs