dt_ility

detectability test

Calling Sequence

[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

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 controllability, controllable subspace, staircase
• st_ility stabilizability test
• unobs unobservable subspace
• stabil stabilization