User`s guide

Choice of LTI Model
10-11
and the conversionfrom zero-pole-gainto state s pace incurs no loss of accuracy
in the poles.
format long e
[sort(eig(a1)) sort(eig(a2))]
ans =
9.999999999998792e-01 1.000000000000000e+00
2.000000000001984e+00 2.000000000000000e+00
3.000000000475623e+00 3.000000000000000e+00
3.999999981263996e+00 4.000000000000000e+00
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 real ized 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]