Specifications

Choice of LTI Model
11-11
5.000000270433721e+00 5.000000000000000e+00
5.999998194359617e+00 6.000000000000000e+00
7.000004542844700e+00 7.000000000000000e+00
8.000013753274901e+00 8.000000000000000e+00
8.999848908317270e+00 9.000000000000000e+00
1.000059459550623e+01 1.000000000000000e+01
1.099854678336595e+01 1.100000000000000e+01
1.200255822210095e+01 1.200000000000000e+01
1.299647702454549e+01 1.300000000000000e+01
1.400406940833612e+01 1.400000000000000e+01
1.499604787386921e+01 1.500000000000000e+01
1.600304396718421e+01 1.600000000000000e+01
1.699828695210055e+01 1.700000000000000e+01
1.800062935148728e+01 1.800000000000000e+01
1.899986934359322e+01 1.900000000000000e+01
2.000001082693916e+01 2.000000000000000e+01
There is another difficulty with transfer function models when realized in
state-space form with
ss. They may give rise to badly conditioned eigenvector
matrices, even if the eigenvalues are well separated. For example, consider the
normal matrix
A = [5 4 1 1
4 5 1 1
1 1 4 2
1 1 2 4]
Its eigenvectors and eigenvalues are given as follows.
[v,d] = eig(A)
v =
0.7071 –0.0000 –0.3162 0.6325
–0.7071 0.0000 –0.3162 0.6325
0.0000 0.7071 0.6325 0.3162
–0.0000 –0.7071 0.6325 0.3162
d =
1.0000 0 0 0
0 2.0000 0 0
0 0 5.0000 0