Specifications

11 Reliable Computations
11-12
0 0 0 10.0000
The condition number (with respect to inversion) of the eigenvector matrix is
cond(v)
ans =
1.000
Now convert a state-space model with the above A matrix to transfer function
form, and back again to state-space form.
b = [1 ; 1 ; 0 ; –1];
c = [0 0 2 1];
H = tf(ss(A,b,c,0)); % transfer function
[Ac,bc,cc] = ssdata(H) % convert back to state space
The new A matrix is
Ac =
18.0000 –6.0625 2.8125 –1.5625
16.0000 0 0 0
0 4.0000 0 0
0 0 1.0000 0
Note that Ac is not a standard companion matrix and has already been
balanced as part of the
ss conversion (see ssbal for details).
Note also that the eigenvectors have changed.
[vc,dc] = eig(Ac)
vc =
–0.5017 0.2353 0.0510 0.0109
–0.8026 0.7531 0.4077 0.1741
–0.3211 0.6025 0.8154 0.6963
–0.0321 0.1205 0.4077 0.6963
dc =
10.0000 0 0 0
0 5.0000 0 0
0 0 2.0000 0
0 0 0 1.0000