User`s guide

obsvf
11-161
11obsvf
Purpose Compute the observability staircase form
Syntax [Abar,Bbar,Cbar,T,k] = obsvf(A,B,C)
[Abar,Bbar,Cbar,T,k] = obsvf(A,B,C,tol)
Description If theobservabilitymatrixof (A,C) ha s rank ,wheren isthesizeofA,then
there exists a similarity trans formation such that
where is unitary and the transformed system has a staircase form with the
unobservable modes, if any, in the upper left corner.
where is observable, and the eigenvalues of are the unobservable
modes.
[Abar,Bbar,Cbar,T,k] = obsvf(A,B,C) decomposes the state-space system
with matrices
A, B,andCinto the observability staircase form Abar, Bbar,and
Cbar, as described above. T is the similarity transformation matrix and k is a
vector of length n,whereni s t he number of stat es in
A.Eachentryofk
representsthe number ofobservable states factored outduring each step ofthe
transformation matrix calculation [1]. The number of nonzero elements in
k
indicates how many iterations were necess ary to calculate T,andsum(k) is the
number of states in , the observable portion of
Abar.
obsvf(A,B,C,tol) uses the tolerance tol when calculating the observable/
unobservable s ubspaces. When the tolerance is not specified, it defaults to
10*n*norm(a,1)*eps.
rn
≤
ATAT
T
,= BTB,= CCT
T
=
T
A
A
no
A
12
0 A
o
,=
B
B
no
B
o
,= C 0 C
o
=
C
o
A
o
,()
A
no
A
o