dt_ility

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